Eigenvalues of the classical symmetric test matrices
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Numbers
$A_n$
$n$
$k$ 
$\lambda_k(A_n)$
Hilbert matrix
2
1:
0.06574145408933511781346312208825067562478390435912563121492449062880550861783159246589681966358488039
Hilbert matrix
2
2:
1.267591879243998215519870211245082657708549428974207702118408842704527824715501740867436513669748453
Hilbert matrix
3
1:
0.002687340355773529231043021276182016424542133863098692155937968190278369564927332837310714104357771481
Hilbert matrix
3
2:
0.1223270658539058465648011426232684263584371445545725142852269466828763762412621778519004217980129621
Hilbert matrix
3
3:
1.408318927123653957537489169433882890550354054915662126892168418460178587527143822644122197430962600
Hilbert matrix
4
1:
0.00009670230402258688555386064623251530253883143735796161129586451170527050745817872412347968393639835363
Hilbert matrix
4
2:
0.006738273605760747950083904081847720004181221483603405615668516694042138359132997771352481155904683113
Hilbert matrix
4
3:
0.1691412202214500324253675226831661964205695694601849768999854125322550758268908606152859454225995547
Hilbert matrix
4
4:
1.500214280059242823215185188779229758748900853809329846349240682452473705782708439079714284213749840
Hilbert matrix
5
1:
0.000003287928772171862957115004760544731399736789023074625349007625523742057608630685063336473000566068094
Hilbert matrix
5
2:
0.0003058980401511917268794978406927228256561451490924692804817440486251791077801905116961870871007486083
Hilbert matrix
5
3:
0.01140749162341980655945145886658934504234843052664014104365560912015099943648451110224623658825348557
Hilbert matrix
5
4:
0.2085342186110133359050025100688200550385820226034301813446785241423546376130408585046786706255991372
Hilbert matrix
5
5:
1.567050691098230795533011005520724633949315252233401435293136702364932743372387396497902870813347650
Hilbert matrix
6
1:
1.082799484565549768538877237225178123400549014943374443763374880714397288400492250810174445709009131e-7
Hilbert matrix
6
2:
0.00001257075712262519492298239799649875540875980451862172338441696902044187819967785533413007808710266051
Hilbert matrix
6
3:
0.0006157483541826576976491993842852714037621133969983790481684036821736941783113585166037274223753125859
Hilbert matrix
6
4:
0.01632152131987582212434507956419150589062565304674253058220442867833289386062837729251654538161996536
Hilbert matrix
6
5:
0.2423608705752095521357284158507011407750642863719227246173905511393670097387505087892305143581960496
Hilbert matrix
6
6:
1.618899858924339096970588147125780071335537525535594460369618501404296099582591915707768212420487677
Hilbert matrix
7
1:
3.493898605991218132935331407976882871187351390557546802079747017070263183120637535279328148361996332e-9
Hilbert matrix
7
2:
4.856763361574250120047893461274345388251265811303823328963823782697703215619703303240797128889431472e-7
Hilbert matrix
7
3:
0.00002938636814592968690453257675107374342930795548961706284835345885431920951200409624854381497817071221
Hilbert matrix
7
4:
0.001008587610770141581225660155444329779883766717260256003944049219594159477101186542262671364395915421
Hilbert matrix
7
5:
0.02128975490832795267586250517224737844312989908304409209201183225624676493790272678501815232708008452
Hilbert matrix
7
6:
0.2719201981493452307327551923882170550890838022638113420282072966830059809741151905877910721421098090
Hilbert matrix
7
7:
1.660885338926931115662155727116417761288185282800217305628242525053928622315917902031466834747528738
Hilbert matrix
8
1:
1.111538966372442427068269060372313499783624290287953692486543847122060230291786629281835610115049695e-10
Hilbert matrix
8
2:
1.798873745817576677264584820179872325977061751599127779425125770587187252040695300307283366685127518e-8
Hilbert matrix
8
3:
0.000001294332091872811480295087156831268144852698134802017913031020726824756385951347534014966446644342848
Hilbert matrix
8
4:
0.00005436943369749942362372444469332109830146161526690310750185084474681708746007437420375174636697755709
Hilbert matrix
8
5:
0.001467688117741867311580993109160768809731877821907741014459057678299908657204845823413081884509250418
Hilbert matrix
8
6:
0.02621284357811904779660478252510828866900693321217959106068111547697235446878758884835087978527463024
Hilbert matrix
8
7:
0.2981252113169307061836778838921031461719483685414693925511022436675434604930573577955069867680548788
Hilbert matrix
8
8:
1.695938996921949452081821727389524336568712318162483425650069959612220344374826060175281419270130813
Hilbert matrix
9
1:
3.499676402911493211337044901103997872361747702814561273141975335020853621493024944569085884564125006e-12
Hilbert matrix
9
2:
6.460905422638582353375637011043934513464286989331662146259042349128930541671950179768360121040249095e-10
Hilbert matrix
9
3:
5.385613348522494181543758161856420018949755714928588341205472210373565311883919942122182401726921914e-8
Hilbert matrix
9
4:
0.000002673013410599413976845435670132068260168507076240730536207578854334292936021854750343587385594966500
Hilbert matrix
9
5:
0.00008758085051459756564812799332025599815394036837284100413649805339379384190249338850386473812295721945
Hilbert matrix
9
6:
0.001978933860215923994220361858474509766852086903710786403474418916546423893888615277426493753046905269
Hilbert matrix
9
7:
0.03103892578126833134497535560603491178144136877781712920573807834726369479843429085590257413972671633
Hilbert matrix
9
8:
0.3216331222992067513228246963618460229465152322794470947609337625325627011515929093478025584169518636
Hilbert matrix
9
9:
1.725882660901846598770796431735064191526174103894708935924529033123914891400655535036383795760984328
Hilbert matrix
10
1:
1.093153819379665763816866910497855568289524646720704101240436482914415996406787555617904477532588842e-13
Hilbert matrix
10
2:
2.266746747762925525271050857529577434334402722123530098847520274774980542431460552489197174236383092e-11
Hilbert matrix
10
3:
2.147438817350478607697119095197277542302208765016711894930568911343879977370408404329361146360845075e-9
Hilbert matrix
10
4:
1.228967738751175049646985272583034427577319563838907618263231990762074337094906521279632497546565066e-7
Hilbert matrix
10
5:
0.000004729689293182347506140586007232260691847768623217786257209926190066937887817137867797837583347062037
Hilbert matrix
10
6:
0.0001287496142763770798087980394071585197760988872361744632992421883541362775420850324618601621456789564
Hilbert matrix
10
7:
0.002530890768670038143719512738223266976179042201033316663942537038824703346692576337111578618999110042
Hilbert matrix
10
8:
0.03574181627163923589058040816590904071382951445989756865357161074895212453476815347298922981211780617
Hilbert matrix
10
9:
0.3429295484835090961538615250313306363368520774790766095021814461259346355901135031951301446064493562
Hilbert matrix
10
10:
1.751919670265177522413757763138644926135331677664644029341210626773049673781249402275449087981719098
Hilbert matrix
11
1:
3.393218595488700528363343214235952480012417127376550182981690346340735862837755110301996276763763193e-15
Hilbert matrix
11
2:
7.807078821441110712382330229623115745306487794593196491582892818427451480715185864934892463950303589e-13
Hilbert matrix
11
3:
8.283328846155649813223400650617404450971665298935435055801794277666602553864729121527414596314563447e-11
Hilbert matrix
11
4:
5.368378366673863276993966018841059450028711055337304961428976426074048015758737257994002878545771443e-9
Hilbert matrix
11
5:
2.371759473940747086393880951743650873778170352466857787336373337413887441274011981666502130769776001e-7
Hilbert matrix
11
6:
0.000007542405920650430387805024246562716220873713773718072528971186482267667471431742916051133272569713873
Hilbert matrix
11
7:
0.0001774285129435782325907793404833537773823833719409312300955067633900753897742790091912280847353368042
Hilbert matrix
11
8:
0.003114434327653221502392009998582825650904629271501487425334075576628652131573038875286294293851294512
Hilbert matrix
11
9:
0.04030962170533794825809027561169419326785539418692112195497446194243772964327952015326305568927133917
Hilbert matrix
11
10:
0.3623821286994223783695746597907466950605836253909549149905977167889040837335790828452267886902517820
Hilbert matrix
11
11:
1.774883179499381619300500445491493002205900840196330874168907338991208003685902911746672644547221892
Hilbert matrix
12
1:
1.047946397962226691925994761796668512344072228932124081890940738355061680944637045702111620098613149e-16
Hilbert matrix
12
2:
2.649021493444886721056139325710665201425710671735133070882210449768535047480619372188232476349192348e-14
Hilbert matrix
12
3:
3.111354897226916735224590679029454807514364654126854236311845452502488491226062529194379541972082304e-12
Hilbert matrix
12
4:
2.251964553490076892299386543277724552642565445941563481248989196337741396239970592556295584455609519e-10
Hilbert matrix
12
5:
1.122861066751703031290978421045009123883303967881855456746509205078789444567427008515983312348768318e-8
Hilbert matrix
12
6:
4.082376110386177344195597615315635191136569970900800834289629126172391766872349177563278826039308195e-7
Hilbert matrix
12
7:
0.00001116335748322442773536348058984485632313722472210433928012690652913669227322975032494557438343400783
Hilbert matrix
12
8:
0.0002330890890217806611181226605005701819970332961970238047489228211001264656809137053509039762862000028
Hilbert matrix
12
9:
0.003722312237891166250385996747397875875371618403079100750387596086090914431013535158946261561209931441
Hilbert matrix
12
10:
0.04473854875218107454748790315123120434565488165744509439844467641488944298196992742111602961127596460
Hilbert matrix
12
11:
0.3802752459550370977932601186194522130377441052048155608755257549517177429491897801525598227193716179
Hilbert matrix
12
12:
1.795372059561997308725147249185634935968847971781747218917866466473103863892050416103112611615030928
Lehmer matrix
2
1:
1/2
Lehmer matrix
2
2:
3/2
Lehmer matrix
3
1:
0.3020195672892079354655471435984374574074930357623897138634169028478460124178023933694276964592889803
Lehmer matrix
3
2:
0.6855348356249378978828360832003576843165454825200883555891726441635414785997836649168049380332856559
Lehmer matrix
3
3:
2.012445597085854166651616773201204858275961481717521930547410452988612508982413941713767365507425364
Lehmer matrix
4
1:
0.2077754859180114429987620704409648149238153060904321099886251691086034686202229360036832017076310037
Lehmer matrix
4
2:
0.4078328841178751665880409632040515615307968887903607309594882174674992044622858928168372434162223908
Lehmer matrix
4
3:
0.8482291554779128241725408974237948059100509971466265920217400965085688598350953560046127914307761951
Lehmer matrix
4
4:
2.536162474486200566240656068931188817635336807972580567030146516915328467082395815174866763445370410
Lehmer matrix
5
1:
0.1560195364491725906236153129875295614238632785189385201984627997592951943334784979700756551543248826
Lehmer matrix
5
2:
0.2727974661560026067151387512774144353787271704027853947423334302079689348938045454022017421133135850
Lehmer matrix
5
3:
0.5010313536665730667448716145351896660308884241356384583284651376725852707443271395807090270832804029
Lehmer matrix
5
4:
1.003511248270376555098852607285504159939901536735103192313813858437803112727098346034732706925287577
Lehmer matrix
5
5:
3.066640395457875180817521713914362177226619590207534434416924773922347487301291471012280868723793552
Lehmer matrix
6
1:
0.1240068312556791442429824857217674447502291396718865782789496547625041965310745739914070516824071213
Lehmer matrix
6
2:
0.1995212628293677298588235458220510185301948739536110581585404505013136574439666853913096850841444619
Lehmer matrix
6
3:
0.3314384820482640455251933264565685183476231137312561902351746815565927083390845912125155404466414273
Lehmer matrix
6
4:
0.5869136993346904636532480991578763491715906284035790856885700065668006978501220712047463882576554495
Lehmer matrix
6
5:
1.156908189230253212151179235810284211875115516470080324674485263418343993347356185423618380587934587
Lehmer matrix
6
6:
3.601211535301745404568573307031452457325246727769586762964279943194444746488395892776402953941216953
Lehmer matrix
7
1:
0.1024674888179524369414393882687446093244470105580128795975455029846439395039095082367236002607059713
Lehmer matrix
7
2:
0.1552141154992177946610359104544706568858111623682257572242962889538651356264571018962847179817075032
Lehmer matrix
7
3:
0.2388024375634534538489006070680397296370330719339934798482237479501390110740401504074865272630127610
Lehmer matrix
7
4:
0.3866345366540771301846713844418312331065454252228170252522847686256834409074201311908865213230639826
Lehmer matrix
7
5:
0.6680246947498320718599314143721939501426182194871181191206320707687836376470303443401151307935904547
Lehmer matrix
7
6:
1.310467314214979485904859035364838206959373468532386146889694999153826489838753918965603889336571237
Lehmer matrix
7
7:
4.138389412500487626599162260029881613944171641897446592067322621563058345402388844962899613041348091
Lehmer matrix
8
1:
0.08707296371264480595292433417309434980989675882454720466781576371060360802943826453916528327247608958
Lehmer matrix
8
2:
0.1260395600012196299422501998776157682608049561502982909461452477479303496980041968411509050608136724
Lehmer matrix
8
3:
0.1832543532116377320361656027128060469408051446875432462302427496975984575719767719687128889624557802
Lehmer matrix
8
4:
0.2760520976020222264469184456570026962017835902639965800033697842337679437655249965986118460263834763
Lehmer matrix
8
5:
0.4393720047478354676283655733327140333260199443077027701567584185828965910750461389592816618103014246
Lehmer matrix
8
6:
0.7460278603243392273963799173776821037348420000074908550221212405225950165118690734731248602349444637
Lehmer matrix
8
7:
1.464868652792320706177031351518026283127485745396960321157142967132259244859444980256201896920755042
Lehmer matrix
8
8:
4.677312507607980204419964575351058718598361860361460731816403828372348788488695577363750657711870051
Lehmer matrix
9
1:
0.07556424727879082759443559191528031350310910697972311653127588430420092080082803411962385063671336289
Lehmer matrix
9
2:
0.1055766277101438744255719212483800948325483753945586139249674437613516619413385020475732214765552586
Lehmer matrix
9
3:
0.1470955979180838573896826048580159983003684752083006178441371092572312075364052445899560251868395347
Lehmer matrix
9
4:
0.2098270347788427515229922096411414568295637793070704318473397115591016825298355896199122811756125629
Lehmer matrix
9
5:
0.3119970567197233564927168324190434686754312119298151677799427061349793757178750193167340831270442759
Lehmer matrix
9
6:
0.4901553640259190373215512024350955906190392537291683646338862996345653736658137548762220758910075149
Lehmer matrix
9
7:
0.8220719884724359484458301098841419869769364263128871742879826157303613937126526810199159769572398131
Lehmer matrix
9
8:
1.620256798445513414158269557820721579130007539058274137312999640680962642402259850122704908751089631
Lehmer matrix
9
9:
5.217455284650546932648949969778179511132995832080202375837468588937245741692991324287357576797898046
Lehmer matrix
10
1:
0.06665733470117610675874260401711783494756047155543962076797716313513497222245807043172844914589211237
Lehmer matrix
10
2:
0.09052495859752886032202671171854976256119837185079569929597519342572303867568592569530565924442530061
Lehmer matrix
10
3:
0.1220130740190772786852386791387557992401505679198736429446557496792409012758871656533318018574789623
Lehmer matrix
10
4:
0.1669937421052730662764886973651550198700267138290433025867294659957918762389132608953724122982617520
Lehmer matrix
10
5:
0.2355147142276372716364065598059764470855954229766066252061389916690874038682891258150638828265562180
Lehmer matrix
10
6:
0.3469632419839606292694728927414888570521654359420042347546772720945295550146288185947710484540433082
Lehmer matrix
10
7:
0.5393289410021374655277393885695263392389715747182890510593527155299901396374717085584838052647986966
Lehmer matrix
10
8:
0.8969430978823659898821754733228515654970155690193359588832912534145932098723265232339313713127425899
Lehmer matrix
10
9:
1.776579330710218340146261202123131596876071047389012197259805990871174412185957093928679141114783613
Lehmer matrix
10
10:
5.758481564770624991495447791197446777631244824799599667241396204184734491008382307193332428481017447
Lehmer matrix
11
1:
0.05957233040797802239248657308288578762383420935618135839990990706650567671413572224291473619367681208
Lehmer matrix
11
2:
0.07903866442071237350915033284502229913223235291321622680511491308309426580977002563681586659087601740
Lehmer matrix
11
3:
0.1037468671187484379243505986210146401988406039200831762170708084903134149160899988449467622036537307
Lehmer matrix
11
4:
0.1374959819763867608185239480508184353752769607876014767130518495634485207116193567762642718795540341
Lehmer matrix
11
5:
0.1862075390997591365431123428427331089871896993259928539103210398544876894460886759754106707932628462
Lehmer matrix
11
6:
0.2605865945482786681071717575895416902030050810355578834696815444203863240114347912697171895644902051
Lehmer matrix
11
7:
0.3811239622338886291155234586885116131037882273221701343594060839538189884263391198019053243536887783
Lehmer matrix
11
8:
0.5871709520182611182975026624117854746513148942154183888419676165594492891799112182635458955146364015
Lehmer matrix
11
9:
0.9711666900091717914034913633762945588567715850076694065065429727425632949874493417291331684230492780
Lehmer matrix
11
10:
1.933723165889705465993489504899345744747975318021297128261893206964178272686610340029864089687776130
Lehmer matrix
11
11:
6.300167252277109595895197457592046647119771068094811966515040057301754263110551409429482024795335766
Lehmer matrix
12
1:
0.05380986333896828639613849272124447842315642250029267036628758528007534020293165286374344549023816065
Lehmer matrix
12
2:
0.07001349040590627379608400749076735323595783052768645136201653835008177795156065682881240169026781214
Lehmer matrix
12
3:
0.08993111068040553599183691755656133018928012833332468877368042892521608543759569012431800985397701532
Lehmer matrix
12
4:
0.1161627752403341903677100104638226075635488797744967390629029815642870611554860666202337184504072717
Lehmer matrix
12
5:
0.1524175857643032574624213139625971638865841584300801346200816255169090798508630601050434735415565101
Lehmer matrix
12
6:
0.2049606012372420908951588349558618362825670484315342821777290959359511056231755498466461640138660839
Lehmer matrix
12
7:
0.2851869743574809514730295104618417027158532760728749956445970400990980539258447559570896578762990789
Lehmer matrix
12
8:
0.4145852777172700844918689244986749362518272910674226403609920928440717880990492815980033098619565260
Lehmer matrix
12
9:
0.6339222286768507543584609824460737605581238448811388838747910354758273866760180057052112023649879286
Lehmer matrix
12
10:
1.045085024156025717498808488052815394255566335437763369833218445244273069240799004666604476618393018
Lehmer matrix
12
11:
2.091567453499131106265672681250100395594637347834758995788217780074813811424322536158110112722355960
Lehmer matrix
12
12:
6.842357614926081751002809836139639041042897436708626148135485350689395440412353739526184027515694635
symmetric Pascal matrix
2
1:
0.3819660112501051517954131656343618822796908201942371378645513772947395371810975502927927958106088625
symmetric Pascal matrix
2
2:
2.618033988749894848204586834365638117720309179805762862135448622705260462818902449707207204189391137
symmetric Pascal matrix
3
1:
0.1270166537925831148207346002176003891670782947084091734124262338865169080630209664807126231413264821
symmetric Pascal matrix
3
2:
1
symmetric Pascal matrix
3
3:
7.872983346207416885179265399782399610832921705291590826587573766113483091936979033519287376858673518
symmetric Pascal matrix
4
1:
0.03801601522913994723751350039950886825691970836959817092875068925094194950441793958977893003894357503
symmetric Pascal matrix
4
2:
0.4538345500256654650971843670379446260149597618472892425844374888571867010487576067481900591641747427
symmetric Pascal matrix
4
3:
2.203446167647323301610075677036603370053836699960584378101109458387238325565767605175217226506269039
symmetric Pascal matrix
4
4:
26.30470326709787128605522645552594313567428382982252820838570236350463302388105684848681378429061264
symmetric Pascal matrix
5
1:
0.01083535906879571811997931617751725008876893928799965330916728242606533874099717496526188460968835024
symmetric Pascal matrix
5
2:
0.1812419014661154161543349360599095438960835638706927581291535221283628990700055403328937828324529924
symmetric Pascal matrix
5
3:
1
symmetric Pascal matrix
5
4:
5.517487909311952245659506526293281282533785090869791540475671991573311678209993532638451548236332616
symmetric Pascal matrix
5
5:
92.29043483015313662006617922146929192348136240597151604808600720387226008397900375206339278432152604
symmetric Pascal matrix
6
1:
0.003004389574741269146001868932782775401585394382359517069482317603389743744349551093651749882602836376
symmetric Pascal matrix
6
2:
0.06429432078606034018176620277763927170740152399383228718735192458517353559945299362258662502855038447
symmetric Pascal matrix
6
3:
0.4893388287436362692575880194982520458061132006153163726810419521210581070679555820550703371874299798
symmetric Pascal matrix
6
4:
2.043573780089088737143751529949701983599737232371291901897615415577580370446098006004012385962230013
symmetric Pascal matrix
6
5:
15.55347327375157723772218671892812564227678985551290881498819192973834656966051052430668233940586153
symmetric Pascal matrix
6
6:
332.8463154070548961465487056599134982812083727931242911061763164603744516734816333429179965625333253
symmetric Pascal matrix
7
1:
0.0008182872282894617116269388603274842735899592000466375819035648620394720555031137288290431776735281544
symmetric Pascal matrix
7
2:
0.02126295980090735313374928456054432862770993310798328620821497921399253732627001597915221468532637740
symmetric Pascal matrix
7
3:
0.2141872319408946031230195020306091017668265208494390145513454022641075088458410511730334925393131909
symmetric Pascal matrix
7
4:
1
symmetric Pascal matrix
7
5:
4.668812379423027459591791610389317055136338188714547830509632774457713514185588922756767147971883398
symmetric Pascal matrix
7
6:
47.03014111691670762021073601529501638597144459333977708311246726587063455507863814353572887474013060
symmetric Pascal matrix
7
7:
1222.064778024690173502229076648864185644224090804788206148036436013331512412508158752826489226885673
symmetric Pascal matrix
8
1:
0.0002200851461416781821578925724482079556938544014975012328289110959588883456223648253861362173832759805
symmetric Pascal matrix
8
2:
0.006720214440293032571432194931466011634180486737582372273842025439723391953600607980616680800936504067
symmetric Pascal matrix
8
3:
0.08373024585804161149546168078610940046795772898826370502309763525465597448328036749113237634835567660
symmetric Pascal matrix
8
4:
0.5118915542490569720681269736488480456203616815418030769116758807781483679626623653016938710662885467
symmetric Pascal matrix
8
5:
1.953538775350564873343292922323241014377679385846285783659425922029120578535483506213372055796399746
symmetric Pascal matrix
8
6:
11.94311553432466249981216100789739515744745872390540011533830624995724062059464057931274381408692031
symmetric Pascal matrix
8
7:
148.8047753363649142782108794874328093997510195594473194840337717609335175722094576217566219266655879
symmetric Pascal matrix
8
8:
4543.696008254266325054316487840407682762745648579131847961527051614511634605915252587118433139018128
symmetric Pascal matrix
9
1:
0.00005864293463646363873113334999598647808758960943728892014296601477301336036474499146065798515596771239
symmetric Pascal matrix
9
2:
0.002056499344492382055884141071115672917747870528681977510644124968337313319979882425602870234111839852
symmetric Pascal matrix
9
3:
0.03039470528307704002512988194581191767002327270400595121551326604084450222481457125431407036691030849
symmetric Pascal matrix
9
4:
0.2373115563550229053521832615549129912061166679936514829210737689737538967424741124210025733213510729
symmetric Pascal matrix
9
5:
1
symmetric Pascal matrix
9
6:
4.213869797828048886078135128049568482981938603212917385314761259114848596604914816851367245023079035
symmetric Pascal matrix
9
7:
32.90046706117506877853487162209766347446936782790689346095447104765885927196546908856353705817979139
symmetric Pascal matrix
9
8:
486.2632233159480718039287091672284237243074166307477511208764852620522271211347363433352905553777728
symmetric Pascal matrix
9
9:
17052.35261842113158174038635566470250774996930153729666133228690830517635628464724644015742496951183
symmetric Pascal matrix
10
1:
0.00001551328374930011502816928628300413951261918113594736113296725580425483714262907838743019582610281386
symmetric Pascal matrix
10
2:
0.0006142088027108703422729453982002348255309844389475548930571765526422110257396650228195018238370053296
symmetric Pascal matrix
10
3:
0.01048573568260852767287802823793635351925063836438178996130096485050641782664074870978683338360530194
symmetric Pascal matrix
10
4:
0.09896498185874359348984583698880188263430294578665531168114689906633336575134656741545246331997355202
symmetric Pascal matrix
10
5:
0.5280379308589448020514432698121590446413015393374484052963961290804083759511289909160804237087238239
symmetric Pascal matrix
10
6:
1.893803345478093704923731086541908746777770106472229734843913277124892817724570556853902480945517745
symmetric Pascal matrix
10
7:
10.10458428040069026363682340390314960157768437973530465753814417735275424080236389438577088273689544
symmetric Pascal matrix
10
8:
95.36765280652495319782423747640485462529251009739922697900184041345614419078419420444291544292808610
symmetric Pascal matrix
10
9:
1628.110824179664395556992920569292253950592416003276544268114899853968803687962214122270673590993986
symmetric Pascal matrix
10
10:
64460.88501701744511018295081921413445255599972068600812535130816814129171043733465862090421094996355
symmetric Pascal matrix
11
1:
0.000004080323410276585565157866420257605310833283156167717924811198053878993258196999501830641218919929879
symmetric Pascal matrix
11
2:
0.0001799867850445881850797769935170220809855149200061994843154014627683178046890330743438645647468227259
symmetric Pascal matrix
11
3:
0.003482807084804635299500460586003127821698215191601300947259609316604865257252975561184742179676653788
symmetric Pascal matrix
11
4:
0.03834486269235352346698877542798337480906772302684259184783744205660744100653936893696228663126014642
symmetric Pascal matrix
11
5:
0.2548873400121343885070483642543014983389055445183026158702763273953687071663463715501098883186168022
symmetric Pascal matrix
11
6:
1
symmetric Pascal matrix
11
7:
3.923301957454588092989564313772651413776877440692809822176209113788575641150365917904993636291464533
symmetric Pascal matrix
11
8:
26.07911281422878387658831573506649505382520899939117590104510695175366859091006107141901934919923086
symmetric Pascal matrix
11
9:
287.1247174048096994788919061166432756090810805967836371772853528635903262258535910763494332652954670
symmetric Pascal matrix
11
10:
5555.963454496226893515793912201861831619132098678609463581062343516791040611715618991263101635758696
symmetric Pascal matrix
11
11:
245078.6125142503822876236921190975275210235287664535830046425633739626469857201422769969413495011196
symmetric Pascal matrix
12
1:
0.000001068193857990405171874714955451924979111539884202149747134237039139897258139715678610215731937442557
symmetric Pascal matrix
12
2:
0.00005194141055464829036314724979119463558227848884134241323750855660139172419885544052238542292747746455
symmetric Pascal matrix
12
3:
0.001123021503801305805690949307783266599496250081144946749252757350605659734940069175566283186072487746
symmetric Pascal matrix
12
4:
0.01409857688764774764555116045674435284235080086297088178694223660536670372919248961867896926903411948
symmetric Pascal matrix
12
5:
0.1114070127409852480872029747691609800905588184399534142255864390826069127973264608286170052534258406
symmetric Pascal matrix
12
6:
0.5404364547044591576548481982999898398375159873117666590948496813051535411953768001525747241640033727
symmetric Pascal matrix
12
7:
1.850356302383146711013370845119865542318673456200840974825766551211798638275240240828727161771897253
symmetric Pascal matrix
12
8:
8.976095628063748394802343278788991507130831946541871887636124078070482643601688386782639046164366573
symmetric Pascal matrix
12
9:
70.92914469091803829558391427891377574072850300893710655956982750320161386689855696721012050044139004
symmetric Pascal matrix
12
10:
890.4548992295415732047822718024174350878853582123316500074486468877288676844620455043364556327864476
symmetric Pascal matrix
12
11:
19252.46136602096897357863519453579899345456021210364015812274737743113158422138734262933253944350107
symmetric Pascal matrix
12
12:
936159.6610200526832137172940769541625135814459380256238110013526417915182795962968334565778802378236
Cauchy matrix
2
1:
0.01899984394510286800534798640667889855856436126944657325380619775951463252802923412162616541220794043
Cauchy matrix
2
2:
0.7310001560548971319946520135933211014414356387305534267461938022404853674719707658783738345877920596
Cauchy matrix
3
1:
0.0006466588800316147202738168390628810253992626804419371280881765632934086795130664390082076546440651749
Cauchy matrix
3
2:
0.04090494848186641366327772745291509130692860826868771259117120266649335794409110263146217510219277162
Cauchy matrix
3
3:
0.8751150593047686382831151223746886943343387957175370169474072874368799000430624975961962839098298299
Cauchy matrix
4
1:
0.00002130658563303825828949183358521967111168319927313177392796801306178020822259444895292480499245988649
Cauchy matrix
4
2:
0.001821255437466873990691844499535681614952888615305823720438814881256432539617009311826477471912063062
Cauchy matrix
4
3:
0.06226782349226395349772705266092407061447325222872811860790708221615926758414736661566261811361058948
Cauchy matrix
4
4:
0.9775562811513028009199582776726216947661288426233595925643928015561891863346796962902246462761515542
Cauchy matrix
5
1:
6.878948830794675219228820091051516459286547041690677188410963745399227633238820963898556722438606989e-7
Cauchy matrix
5
2:
0.00007413674125815791775516825487641463720653498165408058961043661585470826879354253689892327989046870129
Cauchy matrix
5
3:
0.003357591063699839148433906486609342655043469118898130694516977927163620330264856956190015707230751923
Cauchy matrix
5
4:
0.08228541007985516278162157076288768748562708109356503346511334689715181197470114051432581983632651913
Cauchy matrix
5
5:
1.055948840886970427351334098280284116737143652817845252849707064130121986170143802777155517987546683
Cauchy matrix
6
1:
2.189626049639614158680267184150592263396977445777994029049038568895725368810805819329629609928106634e-8
Cauchy matrix
6
2:
0.000002850258897420382036389781401609668988309629378370155455380761655408579382988745307313636124374689780
Cauchy matrix
6
3:
0.0001607660914189997178992153832965731818484230786124860247836937365909431785495222484302229506221825145
Cauchy matrix
6
4:
0.005130954486348264251623103930523538337769745602178129276881364370926178455066516941611095994028356892
Cauchy matrix
6
5:
0.1008467193806321331174132643693028728817600008949378320774613719802281132712859958189896484818166890
Cauchy matrix
6
6:
1.118858687886442686134886439732803564423710886825118724685477898660213667558461288137603525641112298
Cauchy matrix
7
1:
6.897297607880880532512316718054068731690993473620613632296882871894864162411522844333308541076496602e-10
Cauchy matrix
7
2:
1.052765181223297598313782553456430960444343089252685097472040446943804632472238469738169827244076271e-7
Cauchy matrix
7
3:
0.000007114199718268352935525576391102403833538772150281431161056635963299063985305917051103769527058248098
Cauchy matrix
7
4:
0.0002796650552059777363912498092434133933241783767277631230970559105582511994120940190283938373249454899
Cauchy matrix
7
5:
0.007055885770693260665681470071038579961574326639147433958493073238511454413072408452718864318030873653
Cauchy matrix
7
6:
0.1180375605198691566474457230482534479773578478669553670446508902200084103856403757217810688155081901
Cauchy matrix
7
7:
1.171048239916836882051126718294157867386835762170182310383455384989797031939368723852992739580723925
Cauchy matrix
8
1:
2.155309230126522690447216585498343345538668624949550761977271972645024175525204026128175943157199151e-11
Cauchy matrix
8
2:
3.774805026296593178993359262302078463258092913419985254525755052804750874439769101321873228025579053e-9
Cauchy matrix
8
3:
2.974065172465652064978832479053559937803905730170155629907892867090570708162576470928324434376303716e-7
Cauchy matrix
8
4:
0.00001390200487633465333726300929245267122346487625110019696393220896631115350829960000736824648933073017
Cauchy matrix
8
5:
0.0004277939559365934019426508855067328095455802215914148995400588200010974955248544734621384558635662477
Cauchy matrix
8
6:
0.009074627655059752559726047185353838175775422525631959307403409196699512933373673172998486416123381400
Cauchy matrix
8
7:
0.1339932078832854472351390618262769484843063198681868665927306534643789250422405561508971415857149776
Cauchy matrix
8
8:
1.215418738726537935558218644741062122917522106832857470889746764803711100358509255578538059451638890
Cauchy matrix
9
1:
6.692557027702443900104587289876887528790763850834606878159660509033869739092598834401912140477615096e-13
Cauchy matrix
9
2:
1.322939237551671155691490718357924026338765752296880493692994497371895050170073105648393308032939907e-10
Cauchy matrix
9
3:
1.190955614263016772096031690119715178434810804197166773175928577322337715627987121225580093819599429e-8
Cauchy matrix
9
4:
6.455576205760659994586418129769109214345738124620871032113921155393004531761767715180262934268334540e-7
Cauchy matrix
9
5:
0.00002345953068562865041771596843605135919502069823091076274964592839467586174549418137914253858787404456
Cauchy matrix
9
6:
0.0006017053888285795744607524561687148254267212951996852438814222991394013847323539264506403173643144306
Cauchy matrix
9
7:
0.01114793907543788881014172936526442091608379582548682185455590585086213060673150379828864767625402952
Cauchy matrix
9
8:
0.1488513193239686892718329545490535716558654126500287340918180489993537269529693908565859870055190031
Cauchy matrix
9
9:
1.253859046065066299666026435083914816697559866206504676500436650697860321008882159773863265858885019
Cauchy matrix
10
1:
2.067520969985657062611592145296270239907680357310708826421202787151573160840825116189512711478938593e-14
Cauchy matrix
10
2:
4.553219723785809095335566346248796469159281502444735587378259405233343184364074859890600336716901859e-12
Cauchy matrix
10
3:
4.611354214403258829399741324828770984435572688491976399672872333018482383740691931774841577625804694e-10
Cauchy matrix
10
4:
2.844495094858476551645356801609374957436252662648225597177414948239614655578040509963712115562741739e-8
Cauchy matrix
10
5:
0.000001192644663283197899459432691469076351483279428272003078020443275730746032250800153780061872697685182
Cauchy matrix
10
6:
0.00003589955622529550751108393562998283052698622226977529155599524086547337940107782440413060955624943970
Cauchy matrix
10
7:
0.0007980370980435337166805602900224143342587505302147721887352535742631234557677459136743788971748222262
Cauchy matrix
10
8:
0.01324890162321311457795641103810600568121984472258290913708206636213795555407383358737213644936324932
Cauchy matrix
10
9:
0.1627373510986324270787512467816192596903611646176590052553566664682266035812977870136768964622197684
Cauchy matrix
10
10:
1.287662716052689065089608300446554021669937465634329996613704670478278910279311778774398885721139531
Cauchy matrix
11
1:
6.360199794728831781015007068847827898802651237173871333732419176092107090789064304283753036895696194e-16
Cauchy matrix
11
2:
1.544211487346211936140445512383177899959609921037987517178429099164957451241578357995214101693188598e-13
Cauchy matrix
11
3:
1.737888933545691028601354294410293513472154349405479372963829203482257420856157298438244194190842578e-11
Cauchy matrix
11
4:
1.202222239012980341171366344381905895850239845090405519618429996923198120995571652313208461960670430e-9
Cauchy matrix
11
5:
5.714253441535518153622169453270247755148166513384235328187797155247505047871269566433402831128398964e-8
Cauchy matrix
11
6:
0.000001975291118494081837032328190416750846115438403472864599797151877720185049527577190176122510802436406
Cauchy matrix
11
7:
0.00005124085298833561341923359154940584747295570514555884341726234861437867413822612682590083690212193704
Cauchy matrix
11
8:
0.001013711222084831386505807385051735169809957709187217034110434788314171261314712591834342339877253983
Cauchy matrix
11
9:
0.01535888233852972176387841013732748098971342693226300544737702639626959324958844017947329193943071123
Cauchy matrix
11
10:
0.1757611848886057829492515300597785889501028641883851233335553728401623142487711076597908434802323564
Cauchy matrix
11
11:
1.317751619483054672005213777180908244884061767425875697465337667548543203468671379430895757579636261
Cauchy matrix
12
1:
1.949617618370415478654499689632275542313048573563923548327349233692589656981129181234960061451236856e-17
Cauchy matrix
12
2:
5.173704819474801998079578542192982906959118627505936238349126473669949845143969605365128782644936633e-15
Cauchy matrix
12
3:
6.405891380781647418312321932322101884220213072004278383639098322983669492709638312271927802220419348e-13
Cauchy matrix
12
4:
4.911977992825928055499845004274840063911189901566449729214029768162675614638370292068078266834995324e-11
Cauchy matrix
12
5:
2.610403699371329663955352856801999201878829322406265584477764318373406892581416385983792101104453597e-9
Cauchy matrix
12
6:
1.019252340230657534531562603168754481322572216448684770971966892150722617741295055046797384679532285e-7
Cauchy matrix
12
7:
0.000003023354374900090218150577314478788638481810564067663931967583207407701882765816873359187407874242619
Cauchy matrix
12
8:
0.00006943861718898135539940401755161954773925038944143888418058858814654773591901119363375324149386095352
Cauchy matrix
12
9:
0.001245995875375820569681244126966165911654784292276764338436869507096122839958977803534488117805006799
Cauchy matrix
12
10:
0.01746489993055276135799057040184705246785056887683063486054286400619659054372720605243869727041112386
Cauchy matrix
12
11:
0.1880176307841115248900771838499446452468068415587984325869579918345499814939296360814186234740036664
Cauchy matrix
12
12:
1.344804245958331832371322565217119421339448377908180497158334209205710881664127945475121912851648085
Fiedler matrix
2
1:
-1
Fiedler matrix
2
2:
1
Fiedler matrix
3
1:
-2
Fiedler matrix
3
2:
-0.7320508075688772935274463415058723669428052538103806280558069794519330169088000370811461867572485757
Fiedler matrix
3
3:
2.732050807568877293527446341505872366942805253810380628055806979451933016908800037081146186757248576
Fiedler matrix
4
1:
-3.414213562373095048801688724209698078569671875376948073176679737990732478462107038850387534327641573
Fiedler matrix
4
2:
-1.162277660168379331998893544432718533719555139325216826857504852792594438639238221344248108379300295
Fiedler matrix
4
3:
-0.5857864376269049511983112757903019214303281246230519268233202620092675215378929611496124656723584273
Fiedler matrix
4
4:
5.162277660168379331998893544432718533719555139325216826857504852792594438639238221344248108379300295
Fiedler matrix
5
1:
-5.236067977499789696409173668731276235440618359611525724270897245410520925637804899414414408378782275
Fiedler matrix
5
2:
-1.730415809689562522215278495035682647260543185119061039313420088293650580277728329633029698558564631
Fiedler matrix
5
3:
-0.7639320225002103035908263312687237645593816403884742757291027545894790743621951005855855916212177250
Fiedler matrix
5
4:
-0.5577999422106164281564677536428800240843229481257370424088707830798052512542589694913702692613954372
Fiedler matrix
5
5:
8.288215751900178950371746248678562671344866133244798081722290871373455831531987299124399967819960068
Fiedler matrix
6
1:
-7.464101615137754587054892683011744733885610507620761256111613958903866033817600074162292373514497151
Fiedler matrix
6
2:
-2.429488846614513622368589789461370799015534710045707546021895832629347248622403487323972612851513252
Fiedler matrix
6
3:
-1
Fiedler matrix
6
4:
-0.6798226572984700838412478774815258063660200352033690587976687629810769943278573861931620887317681034
Fiedler matrix
6
5:
-0.5358983848622454129451073169882552661143894923792387438883860410961339661823999258377076264855028486
Fiedler matrix
6
6:
12.10931150391298370620983766694289660538155474524907660481956459561042424295026087351713470158328136
Fiedler matrix
7
1:
-10.09783467904461062704442881404673944719277557211303702167644744918514429153770900030921584818039115
Fiedler matrix
7
2:
-3.257639232546274067429806868363273631364726803557465739880705317024495717048269438773103523804055297
Fiedler matrix
7
3:
-1.286208264215581112211200979957398833201745626530751221033698370791955246402429414292878391558242164
Fiedler matrix
7
4:
-0.8405390266420771887271994331527782355225996062428827613471684023669708426888671283379739891447055698
Fiedler matrix
7
5:
-0.6159570567398082607443702059958617196054788013562117572898541800229004620598615853979057602613666879
Fiedler matrix
7
6:
-0.5272040423701743883489880230839924350883323173068007487649879429309607130810692562483013167540792249
Fiedler matrix
7
7:
16.62538230155852564450599432460004430197565872710714924999286166232242727281820582335937882970284009
Fiedler matrix
8
1:
-13.13707118454409017782939655286092361159653263090700514591154713491976706985100761446384224844191782
Fiedler matrix
8
2:
-4.214181652650692989152569842725628403716712178032573807113319795364368905835077537031299389911449105
Fiedler matrix
8
3:
-1.619914404421775020511016076969420469783890372432581130019248875222741231834119358291627773697728945
Fiedler matrix
8
4:
-1.033150028110678162078754329983073116756305552635547817819847128685491918155193660411861211119836733
Fiedler matrix
8
5:
-0.7232313460858447842822290261917872159374221260596265772740321728143288543174524863068220889917047638
Fiedler matrix
8
6:
-0.5890216662283847796777187839674156738266092458106580364653144088579244851737182416187655357624754625
Fiedler matrix
8
7:
-0.5197830649482900173773583439778687026821548706007871467951718170431628439974205409377078888686484746
Fiedler matrix
8
8:
21.83635334698975593090904295667611719429962697647877966139848133290778530916398943906192613679376130
Fiedler matrix
9
1:
-16.58171873876317921324244482081951845523299490243729804813847444076239124339461456571088422542577851
Fiedler matrix
9
2:
-5.298811418105448645671479575343160563075082904562555648694829223434162753399986955357219255769291360
Fiedler matrix
9
3:
-2
Fiedler matrix
9
4:
-1.255120468505402899948612253485958021587974012832835669351861197463196961018065835258312497382133923
Fiedler matrix
9
5:
-0.8520440955209236729698298765465557522521620454695863697489223238465885789043242808288835353890111381
Fiedler matrix
9
6:
-0.6723082603287340797122679442137178979557729917474868105645340199173791452374270860215059892510708700
Fiedler matrix
9
7:
-0.5662371657158971137877253026339257925148430520931155821126032353910201777010611534602322391852103484
Fiedler matrix
9
8:
-0.5159491722125889865557740670412617636851291290295310263875081640880322736333005677581853882745461177
Fiedler matrix
9
9:
27.74218931915217461188813384008409824630395903817240915499873260490277113328878044439522313067704227
Fiedler matrix
10
1:
-20.43172909453070048642468582305390069251743554280163719240932956929138110860656564261318750397502095
Fiedler matrix
10
2:
-6.511375233031686645675253082026810614968322516241189032139853299499775557655634791947134358751618034
Fiedler matrix
10
3:
-2.425919998159591352065542966132501104277188245419115590247162777516573261682431854364032338261120611
Fiedler matrix
10
4:
-1.505306449664106568176367076785007259063512556826453363609625695746930886553345361748999365743302093
Fiedler matrix
10
5:
-1
Fiedler matrix
10
6:
-0.7722159771574114692745335055706742359449050190751701475202410776322060175181880903962245098932883723
Fiedler matrix
10
7:
-0.6298080918412498622977623589423939539603383161347815126692482408413430357663485479783100282237502891
Fiedler matrix
10
8:
-0.5539740933330715779449989397633387123430364052101240951609943134560934305062105172130162626813751281
Fiedler matrix
10
9:
-0.5125428154684582992120088518712042492450378956444657046742594123507025939446539550444701295401081527
Fiedler matrix
10
10:
34.34287175318627626107115260414583082231977649735293663843071438633500589223337876130537449706958363
Fiedler matrix
11
1:
-24.68707503935411442836223453466923035943716321394745978962723716095207080516034304896289458156487779
Fiedler matrix
11
2:
-7.851788789788236414192691021434490048112196158637114062999212029942956186854546353499434960064911956
Fiedler matrix
11
3:
-2.897381139593285153896340406856609408838929318316753378757121836867751141996133744668744063944806899
Fiedler matrix
11
4:
-1.783123147918527657768243556796954131189796672957189216140008311174505235091313170496145906371912455
Fiedler matrix
11
5:
-1.165928996587480977757546891159313813785922453454583331854408961723366754263773429537087174615808017
Fiedler matrix
11
6:
-0.8865678524473151303576797019369637572594724392820398701744338186286778952417053568198324125863401711
Fiedler matrix
11
7:
-0.7065065657874770810967077802324980674232450707729885862454975946700603076278287977665508645642660401
Fiedler matrix
11
8:
-0.6063977091148176277511284836839553051731110160308842147825686314150928994893107923115801832182228249
Fiedler matrix
11
9:
-0.5431082586776423588871703870823483505147399435082149135157344457867509909519209790647233153102412488
Fiedler matrix
11
10:
-0.5105127272589152695552554709283062328778048636034551540299924001579013511096323070528167324884715930
Fiedler matrix
11
11:
41.63839022652781209962499823478066947461238115051068251812621519131913356778650798017981019472985900
Fiedler matrix
12
1:
-29.34774027049051871271008121118965403651742283409627326340470430951427559231768042219610071798112287
Fiedler matrix
12
2:
-9.320002479449347984625171815036071921311985587489218110801402310784883083258700870811329193473821384
Fiedler matrix
12
3:
-3.414213562373095048801688724209698078569671875376948073176679737990732478462107038850387534327641573
Fiedler matrix
12
4:
-2.088243749191113333842377934098756300571904464504725319089542818463555305143565122195317540944576014
Fiedler matrix
12
5:
-1.349198186208549876473623237045694315278262049843747507191451093991486672426209737043055880646718538
Fiedler matrix
12
6:
-1.014251847489193442070051221349198980102052899971711406303832513079824665224663999245771630513396708
Fiedler matrix
12
7:
-0.7943953532404317753068060309073267491792959196732074683620930703930491923033899663077746252952928565
Fiedler matrix
12
8:
-0.6698014359587844231410764510377543333023079663580240355996542769776620164012791584560449512151927927
Fiedler matrix
12
9:
-0.5857864376269049511983112757903019214303281246230519268233202620092675215378929611496124656723584273
Fiedler matrix
12
10:
-0.5364389795804901917900092119347539782943198646101388785447519256296244166247715771945767747145265547
Fiedler matrix
12
11:
-0.5086661900604996355094895208573248990250191963867717610417515261011885429527198744530687760768657346
Fiedler matrix
12
12:
49.62873849166892937546868663345653551358257078293381775033918384493554948665298072790304009086151345
Kac-Murdock-Szegő matrix
2
1:
1/2
Kac-Murdock-Szegő matrix
2
2:
3/2
Kac-Murdock-Szegő matrix
3
1:
0.4069296691827464175186735664726338352224669427521509540375153161792624098178244216216093293004014847
Kac-Murdock-Szegő matrix
3
2:
3/4
Kac-Murdock-Szegő matrix
3
3:
1.843070330817253582481326433527366164777533057247849045962484683820737590182175578378390670699598515
Kac-Murdock-Szegő matrix
4
1:
3/8
Kac-Murdock-Szegő matrix
4
2:
0.5394176951966886469084856520048605577849001452424461685502562050446960600616959512022755654729966944
Kac-Murdock-Szegő matrix
4
3:
1
Kac-Murdock-Szegő matrix
4
4:
2.085582304803311353091514347995139442215099854757553831449743794955303939938304048797724434527003306
Kac-Murdock-Szegő matrix
5
1:
0.3602291941174606581928463059357924338405206458895292869004360161523917637713997314314784790578683685
Kac-Murdock-Szegő matrix
5
2:
0.4572088475983443234542428260024302788924500726212230842751281025223480300308479756011377827364983472
Kac-Murdock-Szegő matrix
5
3:
0.6903428978636519633038768161848324055525347480316966350333035933618453984969610399011286501981623327
Kac-Murdock-Szegő matrix
5
4:
1.230291152401655676545757173997569721107549927378776915724871897477651969969152024398862217263501653
Kac-Murdock-Szegő matrix
5
5:
2.261927908018887378503276877879375160606944606078774078066260390485762837731639228667392870743969299
Kac-Murdock-Szegő matrix
6
1:
0.3521615862880625497914005768314026750582835758941649651946846553240771475038354388927341123239546869
Kac-Murdock-Szegő matrix
6
2:
0.4165814793286884053070918224667408820473930353952203139552609906435473035145171723689334635009231182
Kac-Murdock-Szegő matrix
6
3:
0.5565140713915592866302938183529512430410515018942585624208249315861056109049625280287391000499008036
Kac-Murdock-Szegő matrix
6
4:
0.8462394466036868980373062670466334385466441147399449864348868946328986168846927589103648430432233806
Kac-Murdock-Szegő matrix
6
5:
1.435074342320378163578305604815646081900664922211576472384490413089817241591202033078526787626144509
Kac-Murdock-Szegő matrix
6
6:
2.393429074067624696655601910486625679405962849864834699609852114723554079600790068720701693455853501
Kac-Murdock-Szegő matrix
7
1:
0.3472634716388790321676954077571841963072398630781903729787925700702997154921447135938601802305593410
Kac-Murdock-Szegő matrix
7
2:
0.3933808134856553019472614611452431123519374812699944786720956367674740083428685453624210697350729152
Kac-Murdock-Szegő matrix
7
3:
0.4871719811991667780309117230868103846989290194858510463690716028822760085757655300236267675706904875
Kac-Murdock-Szegő matrix
7
4:
0.6644315121014296442420493137815383002632500018731210788025982441297008593708246309067242340528248344
Kac-Murdock-Szegő matrix
7
5:
1
Kac-Murdock-Szegő matrix
7
6:
1.614062674412915053810689225073218587384812516856884442525306119102825132286306823730854696212102250
Kac-Murdock-Szegő matrix
7
7:
2.493689547161954189801392869156005418993831117435958580652135827047424275932089756382513052198750172
Kac-Murdock-Szegő matrix
8
1:
0.3440626537336433787635056564229723425100973904050475548006495973395340619671204797430976841987778258
Kac-Murdock-Szegő matrix
8
2:
0.3788116993124564814175545428528598779009244176734257063948523062712064401392354206542109335875480187
Kac-Murdock-Szegő matrix
8
3:
0.4464144833937970262227356948177166653367186970719229078290827782401457567561526202728362316302722259
Kac-Murdock-Szegő matrix
8
4:
0.5660777708929858901944912710507637769030145349964821996097614734783059125517077700772902644061093405
Kac-Murdock-Szegő matrix
8
5:
0.7762401141889022543170307945628794517753642110296027882998098866114352322473999978263897303505979905
Kac-Murdock-Szegő matrix
8
6:
1.147533972982192146374748512255722468833669139482468599680376016061773861393500869703020719364407593
Kac-Murdock-Szegő matrix
8
7:
1.769220248683657340696727854196431540377819701493426749070457737808884949029326902157676353820351958
Kac-Murdock-Szegő matrix
8
8:
2.571639056812365482013205673840653876362391907847623494315010204188713785915555939565478082641935048
Kac-Murdock-Szegő matrix
9
1:
0.3418543283920783545553441437957012169925306429276321820649262663577131697263607534182183192656074571
Kac-Murdock-Szegő matrix
9
2:
0.3690305359147481870687907930903903125453167018823900402395457045868285148433560419030924050952372728
Kac-Murdock-Szegő matrix
9
3:
0.4202797552651302677688857449347337495891052918450104431651681622664488184978933817949067847527998928
Kac-Murdock-Szegő matrix
9
4:
0.5068328938652060398090812895008972930283918154046354631926310284732219550039807405580816033457039435
Kac-Murdock-Szegő matrix
9
5:
0.6500258427403912363032023132594509155997231234014322904535653057302683879709719144692842805803102404
Kac-Murdock-Szegő matrix
9
6:
0.8888209218311988629677391557517665052145054464549639164966646478094635136137238223208695125478015579
Kac-Murdock-Szegő matrix
9
7:
1.286575207282272401563847279025087317633345250958924579745339849654838086037086453311791894880415306
Kac-Murdock-Szegő matrix
9
8:
1.903284398388846910154388761656945889211786036258010580071158619130486016538939395217956479011257226
Kac-Murdock-Szegő matrix
9
9:
2.633296116320127739808720518985026800185295690867000504571000415990731537767687497005798720520867104
Kac-Murdock-Szegő matrix
10
1:
0.3402657569055487043217310869498059979047456859860415419315885013555043330223420043419156712010116626
Kac-Murdock-Szegő matrix
10
2:
0.3621300701981664700115171841492889719174954456227785954781890194974235705566636479977791034040062579
Kac-Murdock-Szegő matrix
10
3:
0.4024394345522692883598140883680690756580339260902950050128571431080650573510696575062648142735120909
Kac-Murdock-Szegő matrix
10
4:
0.4682139160984765485699879261475937201877891048705893638335056349915614437636160919937583720216203001
Kac-Murdock-Szegő matrix
10
5:
0.5721909497067887882469746263403275007396413925468470333446812345110562455959376441833710630204964492
Kac-Murdock-Szegő matrix
10
6:
0.7368233517065452307454516034693872175479090685679008918583388337322441359048963151884388342429169545
Kac-Murdock-Szegő matrix
10
7:
1
Kac-Murdock-Szegő matrix
10
8:
1.416032158924191308354902573179706980255722210329189412432129752563407815147203264562237466521311750
Kac-Murdock-Szegő matrix
10
9:
2.019088233835393219071480198341797425697578995376816419710873121025374364030650693968448451504979797
Kac-Murdock-Szegő matrix
10
10:
2.682816128072620442318140713054023110091084170609541736397836759215363034627620680257786223810144737
Kac-Murdock-Szegő matrix
11
1:
0.3390844441072130565568879037962417166921015703310766035051520882392506585242869497815136436354929496
Kac-Murdock-Szegő matrix
11
2:
0.3570719163075859458565777934413595902250019081870210873981258221229250278597152833830420969430753922
Kac-Murdock-Szegő matrix
11
3:
0.3896766873054063531194176875152891034432681494014470706812465903920621413083121867441640459017555927
Kac-Murdock-Szegő matrix
11
4:
0.4415226086524152895848246098523196072390105934985341860748317485418589113294897522638393423760596032
Kac-Murdock-Szegő matrix
11
5:
0.5206865752215220888688423084417896736930234234044105982877143256233396086645363910150092996379311817
Kac-Murdock-Szegő matrix
11
6:
0.6408706261975133678755539491048081050590952244159309265939966473785202541655712763645697562548783236
Kac-Murdock-Szegő matrix
11
7:
0.8248582714435521087581983514675042172792856282317406189089819123277150379029097298743957071349455024
Kac-Murdock-Szegő matrix
11
8:
1.108259825733896007194215086974885882997294624594177432039779184294619647999142451478116710704325053
Kac-Murdock-Szegő matrix
11
9:
1.535570207487226260449539534623621185290329799689547493428336288539918313145871069014447012602341971
Kac-Murdock-Szegő matrix
11
10:
2.119267210608589389488828560626626814479597649304336367893266597662076158646081236510432093721661628
Kac-Murdock-Szegő matrix
11
11:
2.723131626935080132247114214155554103601991428941777615188568794877714240454083673570470291087532803
Kac-Murdock-Szegő matrix
12
1:
0.3381819111359867091298671755217522535036661528226488280384400992114863793677701851073628091506467362
Kac-Murdock-Szegő matrix
12
2:
0.3532494072064958883220553214188547422863112058963468117268497559078658395522775680310651137083943058
Kac-Murdock-Szegő matrix
12
3:
0.3802082859866093027476353283367207517817271942369150747862502801772958194576459059276983563156004409
Kac-Murdock-Szegő matrix
12
4:
0.4222344039311917034320672413878846035909849841928278512664288362382806075072297725059938638094200261
Kac-Murdock-Szegő matrix
12
5:
0.4847062144631083672761671327059041174747139520322655122969580060070233506714531767222715933102480153
Kac-Murdock-Szegő matrix
12
6:
0.5764363412373473862014661112713217215760341364214624549018569862850089298881101359968969197175744690
Kac-Murdock-Szegő matrix
12
7:
0.7116782452262894907108413298383309722815008248308749283335451590718671532703999663083901670357741425
Kac-Murdock-Szegő matrix
12
8:
0.9128998656267962352421512683557216349233437973603709463622593692026490329785530836691972075291471696
Kac-Murdock-Szegő matrix
12
9:
1.212569702026080189448080015793701781222526323441989354465490958141430127187385252998205149876712967
Kac-Murdock-Szegő matrix
12
10:
1.645330271069701925735546211923474467347508523066717032040047190385191090630367757216800164939667987
Kac-Murdock-Szegő matrix
12
11:
2.206151734911925940687409017803590123735865552635306302079315497390897170045345512936071924311017699
Kac-Murdock-Szegő matrix
12
12:
2.756353617178466861066713845642742830275817353062274903702557861981004499443461682580046730295796042
Minij matrix
2
1:
0.3819660112501051517954131656343618822796908201942371378645513772947395371810975502927927958106088625
Minij matrix
2
2:
2.618033988749894848204586834365638117720309179805762862135448622705260462818902449707207204189391137
Minij matrix
3
1:
0.3079785283699041303721851029979308598027394006781058786449270900114502310299307926989528801306833440
Minij matrix
3
2:
0.6431041321077905561056004899786994166008728132653756105168491853959776232012147071464391957791210821
Minij matrix
3
3:
5.048917339522305313522214407023369723596387786056518510838223724592572145768854500154607924090195574
Minij matrix
4
1:
0.2831185828579485568938626513169628962574215260465577910563016176955100888505305767301161195926051742
Minij matrix
4
2:
0.4260220477604618364849149382732778761260810227347931848744611619232942894521621404144417676945055690
Minij matrix
4
3:
1
Minij matrix
4
4:
8.290859369381589606621222410409759227616497451218649024069237220381195621697307282855442112712889257
Minij matrix
5
1:
0.2715541293388211794435851935411741752573699717541074567578672228933754954759604895323616576551206244
Minij matrix
5
2:
0.3532532828937385405483538901162490337116225353864942931227487973350301538139143988832754322821330201
Minij matrix
5
3:
0.5829644982937404888787734455796569068929612267272916659272044808616833771318867147685435873079040087
Minij matrix
5
4:
1.448690569796642576948170203428304704419464659158376689378560918433875570998066872334372031972403449
Minij matrix
5
5:
12.34353751967705721418111726733461517971858160697372989481361858047603540258017152448144729078243890
Minij matrix
6
1:
0.2651878342412025665786917688119647164664473909426404092122155987637456686479583587260828964329667135
Minij matrix
6
2:
0.3188643842942824857111356057021933322928178809729312460524854954273825861397455175647998997263670301
Minij matrix
6
3:
0.4462147547781042619333522662848200027678860779217696952001690390564590407528278445861430837348885200
Minij matrix
6
4:
0.7747192223207199386899027962269754151374250965224743638114827216118779198666876836762263147859179723
Minij matrix
6
5:
1.988156536964751749042108514890439922328736923978092764906836054273243316442629099192305068316815822
Minij matrix
6
6:
17.20685726740093899804480904808360661100668662966209152081681109086729146815015149625444273700304394
Minij matrix
7
1:
0.2612950729772454797317774299018729444690855401782657481592736103713903264186482163518823270381493205
Minij matrix
7
2:
0.2995571455553918815428485986828446672405417733602474100012622395506865415533831972765755777968639002
Minij matrix
7
3:
0.3819660112501051517954131656343618822796908201942371378645513772947395371810975502927927958106088625
Minij matrix
7
4:
0.5583650395238060382223542264417458783278226617641056304862401625760050453923272865760456310679393046
Minij matrix
7
5:
1
Minij matrix
7
6:
2.618033988749894848204586834365638117720309179805762862135448622705260462818902449707207204189391137
Minij matrix
7
7:
22.88078274194355660050301974497353650996255002469738121135322398750191808663564129979549646409704747
Minij matrix
8
1:
0.2587359302721336156095611346767629335476081598993982572650974377549263914993043037611778556815363342
Minij matrix
8
2:
0.2875200897756846126508704366109105611952391640978979277422844720659119165844485967471370079254434739
Minij matrix
8
3:
0.3458440443267058962609843322705213857171874030280660118419320660827226483617597580360624950310108584
Minij matrix
8
4:
0.4577629624332251724210875200969196998888890195224094887048399296684988681840343473072364759124296722
Minij matrix
8
5:
0.6883856848346758640072500941671349419218152708576345737333714849519261182824892034925589441433692190
Minij matrix
8
6:
1.258287827212876303673328465384723554009644509250096446127861985183088247008768622147703389500373872
Minij matrix
8
7:
3.338165566772760286594207540255389042909755140743341665100933744497399947334117635560084218893193160
Minij matrix
8
8:
29.36529789437193824878271047653763788080986133260115562948367887979552586274507753294803961291264341
Minij matrix
9
1:
0.2569614397922604819342940647211475600112941991530704986071858743342612563837387720312657404975498514
Minij matrix
9
2:
0.2794637969315703083680457795039177452129807788088893782794595229475305667110410079609212398856574045
Minij matrix
9
3:
0.3232170369606074079641630291114250835382037577620753757956471831127878254534839063809325136018857847
Minij matrix
9
4:
0.4014498805183397520296134817885648161826097554323258231999071020467176208206259172664548816866808924
Minij matrix
9
5:
0.5450062602497477820853111191273193905757132365914098189396561079348392563234336456969410027835676024
Minij matrix
9
6:
0.8356947625045126777072109027344930421570418618710419707544615626505970504085021263690454630166734477
Minij matrix
9
7:
1.549338234320310762028667959490830322803649599430402222962505611012628878005460801533139573106380235
Minij matrix
9
8:
4.148473921698289372472358885159409483421957130304083830079051420954115262258152884829366761485608475
Minij matrix
9
9:
36.66039466702436145541033477836289255609654968064670108138212561500652228363556093793193282393599631
Minij matrix
10
1:
0.2556795627964359430424419021292221777613884841798559698846303329939992748348838230631300587544137886
Minij matrix
10
2:
0.2737867616392448730888275770970182346419269978586968528758035402208853326301523454075051163831044353
Minij matrix
10
3:
0.3079785283699041303721851029979308598027394006781058786449270900114502310299307926989528801306833440
Minij matrix
10
4:
0.3662088746157992056779597035428285861467880965071193861415436437213174670143362251592224222395713187
Minij matrix
10
5:
0.4652330878085648183393624256879067911695405354731651309376154037503411304119255187558397215387897293
Minij matrix
10
6:
0.6431041321077905561056004899786994166008728132653756105168491853959776232012147071464391957791210821
Minij matrix
10
7:
1
Minij matrix
10
8:
1.873023060424910674201623534873456143862393308657721327402864291713075181233278604081006666642615225
Minij matrix
10
9:
5.048917339522305313522214407023369723596387786056518510838223724592572145768854500154607924090195574
Minij matrix
10
10:
44.76606865271504448564978485666956806641796257732344133275754278760038161387542348353329601444150550
Minij matrix
11
1:
0.2547229082054579470937810391051771802451017889424388116553870084252218010536491620364453382878923117
Minij matrix
11
2:
0.2696261691255752116285793669768277409992809600386736367173700553580044702117874958688209368728609732
Minij matrix
11
3:
0.2971674339174338502760763969815066989013817996103863308577192924760837194853683898944495856672863928
Minij matrix
11
4:
0.3424504984907850991602540809745215632822631703374787791731124977356647437889038425971180591267225647
Minij matrix
11
5:
0.4154701082357982564856029716247761838416853074730059881435285304618621390137455465400365793860289824
Minij matrix
11
6:
0.5366202617201654560185258966012890261931868446204545086861237028925545690283019781015825110939647544
Minij matrix
11
7:
0.7517436078482347571114899177558717966443210623664078194848909115225745887146792420476718605630816812
Minij matrix
11
8:
1.181140462210391807748775438054962564453278741965878069854454742764211174531332974039170319171477992
Minij matrix
11
9:
2.229269594400635045474597689130977188169588846650443593085597975849087364069059683976048107185359093
Minij matrix
11
10:
6.039471680218929239954068023790091173577855073358320333020790004439469341082436955138738884973674486
Minij matrix
11
11:
53.68231727562659332904824917900399888369205640463651212932102527807526608902073472975991781767165077
Minij matrix
12
1:
0.2539897779646450051704716444527092299005872675682504661689702398651783123337430161072892913446504374
Minij matrix
12
2:
0.2664809571473204952136173254213705270582993684854310405010923582900296522574665517134183353687112818
Minij matrix
12
3:
0.2891897470376321109627941270649340113749433116167808157191650854410265068262513029748483736207392267
Minij matrix
12
4:
0.3255575444018983985624032671916632754166395338365791537904662550827507406623576653801450435246760703
Minij matrix
12
5:
0.3819660112501051517954131656343618822796908201942371378645513772947395371810975502927927958106088625
Minij matrix
12
6:
0.4704595974580569646218645584205404620413264912388162285824512597492291935057795329577608681801372898
Minij matrix
12
7:
0.6152947366021968171565006310490423797463717709906642842555631346891650687773697690016956067281340108
Minij matrix
12
8:
0.8707453295489459086242664343745055696695582526116026184451452260343186768680339233943676331184244067
Minij matrix
12
9:
1.379021186904885918531895225764088674971310362639570524992617346675226390776706201182663607416592577
Minij matrix
12
10:
2.618033988749894848204586834365638117720309179805762862135448622705260462818902449707207204189391137
Minij matrix
12
11:
7.120122174523142507998694445030045414662406849572712073079279330996103792248852341691961084799165188
Minij matrix
12
12:
63.40913894841127587315749234123110045515855679143959279446524976317697166574343969559585015589876951
Wilkinson matrix
2
1:
-1/2
Wilkinson matrix
2
2:
3/2
Wilkinson matrix
3
1:
-1
Wilkinson matrix
3
2:
1
Wilkinson matrix
3
3:
2
Wilkinson matrix
4
1:
-0.9142135623730950488016887242096980785696718753769480731766797379907324784621070388503875343276415727
Wilkinson matrix
4
2:
1/2
Wilkinson matrix
4
3:
1.914213562373095048801688724209698078569671875376948073176679737990732478462107038850387534327641573
Wilkinson matrix
4
4:
5/2
Wilkinson matrix
5
1:
-1.114907541476755798515614060708543968123756263387176208658987111839571202959207342942475845886297288
Wilkinson matrix
5
2:
0.3819660112501051517954131656343618822796908201942371378645513772947395371810975502927927958106088625
Wilkinson matrix
5
3:
1.254101688365052412129777879843072470905915260811144893256074509214811256443923946707095709738439529
Wilkinson matrix
5
4:
2.618033988749894848204586834365638117720309179805762862135448622705260462818902449707207204189391137
Wilkinson matrix
5
5:
2.860805853111703386385836180865471497217841002576031315402912602624759946515283396235380136147857759
Wilkinson matrix
6
1:
-0.9605048700187634919796447883536626456827815054566913217684094305444602647103620552456106085172862995
Wilkinson matrix
6
2:
0.2530203962825329389499902319915203787354505382071957892689011218062926950870254308481149853468292567
Wilkinson matrix
6
3:
1.260876721743445535749916496686517413083856957863813225226936729546859586600387902085698252635382367
Wilkinson matrix
6
4:
1.945041867912628808577805128993589518932711137529089910623974031794842464057094638149162105216145913
Wilkinson matrix
6
5:
3.199628148275317956229728291667145232598924547592878096541472700997600678109974153159912355881903932
Wilkinson matrix
6
6:
3.301937735804838252472204639014890102331838324263714300107124846398864840855879931002722909437024831
Wilkinson matrix
7
1:
-1.124885419764574157919539736732375418401411317964527985204859518961905865399207179236015899044733122
Wilkinson matrix
7
2:
0.2679491924311227064725536584941276330571947461896193719441930205480669830911999629188538132427514243
Wilkinson matrix
7
3:
1
Wilkinson matrix
7
4:
2
Wilkinson matrix
7
5:
2.363328237932683570374168609319887919577757617093584909906785754315325562623077670634585170305540097
Wilkinson matrix
7
6:
3.732050807568877293527446341505872366942805253810380628055806979451933016908800037081146186757248576
Wilkinson matrix
7
7:
3.761557181831890587545371127412487498823653700870943075298073764646580302776129508601430728739193025
Wilkinson matrix
8
1:
-0.9639679302095880241681711669849620418351052578045838591647355422865370162963296405829075899263940001
Wilkinson matrix
8
2:
0.2160021298579287480670518619858569419698348201518512290911440648283816631201547696947057457787122153
Wilkinson matrix
8
3:
1.103086596453912105344122926223558836852663658385278354256305477982182424098044547214511781397922317
Wilkinson matrix
8
4:
1.714738551506434641507148336116960129958071419592584266546058241566509091276470982974592098732092580
Wilkinson matrix
8
5:
2.618615731219713558217733853187624362842856951084059008882932961406119049024610721867890408445397665
Wilkinson matrix
8
6:
2.818458896574720740845759335020047388865633782417075836236780267698646338242633184338306258610514299
Wilkinson matrix
8
7:
4.242265602535962360606314387573778842139584648335246496025497102898235543173674371500505400083074018
Wilkinson matrix
8
8:
4.250800422060915869580040466877135539206459977838488668126017425906462907360741062992395896878680905
Wilkinson matrix
9
1:
-1.125422415673318461333545613686413613711005262934823288410515284431688636878676873469042711814797331
Wilkinson matrix
9
2:
0.2547187598258609234931078881464909446587699528422625831708481502992884594845991948468659558389407145
Wilkinson matrix
9
3:
0.9525842190752136956760904628227529568727807162827664658458673696327483494981362836867653154796361361
Wilkinson matrix
9
4:
1.822717080887108155688456219118133469722318165623200284292047499034512818098083360276495460042762038
Wilkinson matrix
9
5:
2.178284739549980945708254849001260424028474938391658344069479317244257270877416451018364448284043946
Wilkinson matrix
9
6:
3.177282919112891844311543780881866530277681834376799715707952500965487181901916639723504539957237962
Wilkinson matrix
9
7:
3.247396472578982543098109829829336424284572583306037834165155175371406930012515012717364942653899858
Wilkinson matrix
9
8:
4.745281240174139076506892111853509055341230047157737416829151849700711540515400805153134044161059286
Wilkinson matrix
9
9:
4.747156984469141276851090472033063808525177024954360644330013422183276086490609126046548005397217391
Wilkinson matrix
10
1:
-0.9641272045307894077107491347846532174176537223182655903010155719182320180852450143709722320873536169
Wilkinson matrix
10
2:
0.2128275024018603980602062221291861247025022228207976637167297240435198814026699830482080339370675464
Wilkinson matrix
10
3:
1.080095801937937940468895241670763252259072051338076434817339558784353913901531178562297417969325342
Wilkinson matrix
10
4:
1.661429949346466453734476884784026963063953809675259848028286745058706624700812625786984503868719636
Wilkinson matrix
10
5:
2.438289627105229035668968553050644309071646513753228506730222619982787844528401816039325333493656450
Wilkinson matrix
10
6:
2.655067652107352842033145822563209172789615755665262309604581845665049386103769737501296849569040255
Wilkinson matrix
10
7:
3.699744918183057302140165286792607295643493689379301130138018007239351094367226270161918402377716842
Wilkinson matrix
10
8:
3.724263636207576008068604759575707228564912492006917568590427875493546992471111289355111348848802011
Wilkinson matrix
10
9:
5.245996857304565129432720053270638360443441467847659518615435385911739165288085749607431078246654983
Wilkinson matrix
10
10:
5.246411259936744298103566310947870510879015719831762610059973809739177115321636364308399263776370552
Wilkinson matrix
11
1:
-1.125441061096268591060513292111545033783251203388543243034978711595096666923300619808158237984755225
Wilkinson matrix
11
2:
0.2538424544194282798944846042300248616264218796370732979745274329471982467441442170475104123280461551
Wilkinson matrix
11
3:
0.9478141960026713351788779832608885954355620734509442969383468780350426272683857376267237203892575463
Wilkinson matrix
11
4:
1.792267109477062326576742450429731650483389817273655340262437077241570561079315465323159794793759197
Wilkinson matrix
11
5:
2.135547441131822168467758438491012352847386618558241182262250714940712951677685154050248503909342055
Wilkinson matrix
11
6:
3
Wilkinson matrix
11
7:
3.081977031997906812197620331880126276810005987380415910762761166995541951446667074857546062630728258
Wilkinson matrix
11
8:
4.207732890522937673423257549570268349516610182726344659737562922758429438920684534676840205206240803
Wilkinson matrix
11
9:
4.213870558154003439036473391015633288034529426186466180418681421552596357071222201125082750918602689
Wilkinson matrix
11
10:
5.746157545580571720105515395769975138373578120362926702025472567052801753255855782952489587671953845
Wilkinson matrix
11
11:
5.746231833809864836179783147463884520655767097812475672652938530071202779459340452148557200136824677
Wilkinson matrix
12
1:
-0.9641320648509151058867771657310052555881581509703413758116817254523969007807968568569413770819795561
Wilkinson matrix
12
2:
0.2126681619687114614486669912773339041710261255285926853673405762935920229066809229529174158702362103
Wilkinson matrix
12
3:
1.078253941559900241405401277986209813730732904348264156268180299916255308898715373984492630805952283
Wilkinson matrix
12
4:
1.655144917803647356081284637815206506176171137482635131304708961440302764366684150793108975745671310
Wilkinson matrix
12
5:
2.404330257855741697471439344634392125241040456391269119521482718888707301219395302724707822383268107
Wilkinson matrix
12
6:
2.618274263981897653494180572157290696523740048015558008714669290026485186772145329406134496904372189
Wilkinson matrix
12
7:
3.525407151414310776067459342539844653021613374841579044283503708591185166131090019399089260722914940
Wilkinson matrix
12
8:
3.556208747746085385960920891335829901864108253377169995206193612340102668645743444703125597023100578
Wilkinson matrix
12
9:
4.709952998060969576758140210048106593872037165630351845440878326472917305945200906535117799191557665
Wilkinson matrix
12
10:
4.711502847974355363593622654706880446689912773960279465739691241748300142385519670328772407759975636
Wilkinson matrix
12
11:
6.246187715959992814184336990522452069722734249758877210297636671583331818586395254213533863978286561
Wilkinson matrix
12
12:
6.246201060525302779421324252707458544575041661635764713667396318151217214923226481815941106696644078
Moler matrix
2
1:
0.3819660112501051517954131656343618822796908201942371378645513772947395371810975502927927958106088625
Moler matrix
2
2:
2.618033988749894848204586834365638117720309179805762862135448622705260462818902449707207204189391137
Moler matrix
3
1:
0.1206147584281832318917814453505370601275837314710707338194266744515575780082210821005082203241038651
Moler matrix
3
2:
2.347296355333860697703433253538629592000751354368138774472482756264131644278029470843033226314799148
Moler matrix
3
3:
3.532088886237956070404785301110833347871664914160790491708090569284310777713749447056458553361096987
Moler matrix
4
1:
0.03335894894182139229169481986683632008781701062654249201449947813205979779672140235746413645122227249
Moler matrix
4
2:
2.297411936243863662223675454687378523991097958128332309949479820165595822891314425439210965710408041
Moler matrix
4
3:
2.547709749744225106454486607261931996051534240245594569605009647226357121228629220945529818487972138
Moler matrix
4
4:
5.121519365070089839030143118183853159869550790999530628431011054475987258083334951257795079350397549
Moler matrix
5
1:
0.008646272283959250274621111327247633723394052451807327631196617369240080530483532222550680727950286532
Moler matrix
5
2:
2.278450482604586477859457816221396424547999283494701418508221900648778980639179293516534786547112615
Moler matrix
5
3:
2.396468531986137929259164637376520406276937948650102848016112575310453300028084373168357512076656384
Moler matrix
5
4:
2.828934782420331234475106126686112405618378114253266941618524340349607732945365906295393540932551061
Moler matrix
5
5:
7.487499930704985108131650308388723129833290601150121464225944566321919905856886894797163479715729654
Moler matrix
6
1:
0.002186606787320431301718202604350976570759644388938865820962646894130710586544481969293142847023671812
Moler matrix
6
2:
2.269066791978828526430878887975608460253946225080824945850386653498936298239221025246777233457333613
Moler matrix
6
3:
2.339842992234456953854172365149105647540162794423251735101184037002009173027611735333804258166112315
Moler matrix
6
4:
2.529934240439879995357883867634249826926401563403884169546765379044164762326929663608156201893616866
Moler matrix
6
5:
3.191812772267186656820325371010062292417798180231420452058707561103199746659836879419039600370800118
Moler matrix
6
6:
10.66715659629232743623502130562662279629093159247167983162199372245755930915985621442292956326511342
Moler matrix
7
1:
0.0005485467458864066701841649915195248974012629375225399460299478581845519068094971234065164537186620422
Moler matrix
7
2:
2.263701097781094784571292029851303805733155888875082685107672727429397200235526519271237345482216451
Moler matrix
7
3:
2.311523128749914589350090416057461121842471719740321939421768747978566805964147070924418392676901842
Moler matrix
7
4:
2.422014144659872139042896134027986933456958425600331470368461257360152285636068600135314475313666598
Moler matrix
7
5:
2.694789283934211389887980592749451944861273703251362687287747042803182693746355679187339729156570385
Moler matrix
7
6:
3.639022741896820126205068322185909308528484545150969581390414370252527612797942775035773571879404070
Moler matrix
7
7:
14.66840105623220056427248834013636736068025445444440909647790590631798884971314985832250996903752199
Moler matrix
8
1:
0.0001372746490051367935357045224883634270959717819583814576327400242529520420039961379533742011553388276
Moler matrix
8
2:
2.260334007608730769762846188544527851915723191000934155551738592448491997680917253014733072492385387
Moler matrix
8
3:
2.295059673488905366074460642486222286803393868399076911824179563306081000294436675364075508080707897
Moler matrix
8
4:
2.368603295490823752946229946145120430600436169293409543781601938894167413917744301524206071373954598
Moler matrix
8
5:
2.521812530633157557749705722998792805249217768049794496560539187760021950692776998721796855063759203
Moler matrix
8
6:
2.890523242010896050241501373612939813072291752318335600107358275110976442788947363356745159814371891
Moler matrix
8
7:
4.172870774097098011434461512458230392010991534724106198221767817160727877707541828204807534449001602
Moler matrix
8
8:
19.49065920202138335499725890923167805692084974443238471249518188529528036487563158367568242452466408
Moler matrix
9
1:
0.00003432847792555303487447885641227544086457904064448328463179408749830248538429688799717621731901986881
Moler matrix
9
2:
2.258078166412059148074733059986489537149058745310215250170782394388247779807834052322569468174508720
Moler matrix
9
3:
2.284548841314735483816930408076750366732675527993440811567771308404353864328571050207350972598698316
Moler matrix
9
4:
2.337577623745897075521489998865664541364652582117292940761233054529773820179168029557271502467614353
Moler matrix
9
5:
2.437515913961790378641198177198413724589075875053502370862928458171424549074292516021584368961829463
Moler matrix
9
6:
2.638200195016628650034528204144728869289598396579116081872389647611978478099903241058428562108598058
Moler matrix
9
7:
3.117260542498012209414216565229539799240503221248506683213377668857067926399690955036887451347668811
Moler matrix
9
8:
4.794996521218868649285903284696932658712488464412556347924787868745886964916871430967580596904529397
Moler matrix
9
9:
25.13178786735408285217612582294506822748108260824472503034209780520376831470828442794032990121923386
Moler matrix
10
1:
0.000008582806924387461973323317227117662494975163715191276372365617930666078562882760626486536734242237875
Moler matrix
10
2:
2.256491197976440456186408809029451179867613944955165314908854808282713847146911683469572110756546746
Moler matrix
10
3:
2.277391114561907916752689603754274314424093742346664607279077122689248197883923990204534864721261433
Moler matrix
10
4:
2.317701565913527057661908101150078578399111626042946307929627875191614458686909464552495727701233678
Moler matrix
10
5:
2.388872416162980907784606939200580542735384823790287070285570522646617889214848213278643067797439971
Moler matrix
10
6:
2.517158244085982542678439922837048060586009862053233338855422295556918641398314561837366777582022022
Moler matrix
10
7:
2.770820080727843711946945770981153747413703124624771630473419039053952146817657205385851048980284537
Moler matrix
10
8:
3.375284311029063063881550776971688869299987090802503073981965056630236374284580256641307420931652656
Moler matrix
10
9:
5.506462744838395468455062652569183597567117403790809460821701746647539023814305268519826647035999670
Moler matrix
10
10:
31.58980974189693448719041410018931399204448340642990400418798916768322875467398647334977584795682504
Moler matrix
11
1:
0.000002145749306447795880801748323163583235814429465696122417756039598085380076379806900394751178764068556
Moler matrix
11
2:
2.255331601719994062989525518240852305363703122762607281897324995635038525818355410326349944355021234
Moler matrix
11
3:
2.272280047923125833666605849766536076859137446682666376098284007835103873542562479263877738184944507
Moler matrix
11
4:
2.304094026234073336592205170860450583732857164143905888308167376442818091264893515240659986019091786
Moler matrix
11
5:
2.357776934606288697757950667040112243767661122499367680211824784675790499380464811017916508528686070
Moler matrix
11
6:
2.447897893994441692218720819328196221515941364479359534462195780443901520557485083726318605265803595
Moler matrix
11
7:
2.607043070709689183740318652470113802729431718827614859896604237260649123694401782690231774717412022
Moler matrix
11
8:
2.919573417802183055019127156282407924070733155527722793130024153155254112456694204128074162880809164
Moler matrix
11
9:
3.664887626937574486393357711266232857980667759890826210288494639497428538497594514800335405671753299
Moler matrix
11
10:
6.307913390192422070031408272961927921674637455378603639283996706550100496282802134173713473109862827
Moler matrix
11
11:
38.86319984413090113379489938003484689872199387537786004030066556246431713312466968482562200651543673
Moler matrix
12
1:
5.364405879543367768026408537741394516788696502237965012436564338620477500417578451040852967167124479e-7
Moler matrix
12
2:
2.254458137014795511368230841426803631165428346503747703137932648394934811641865280309760321742205204
Moler matrix
12
3:
2.268494793740956721979978789794304361168580809477436760043018632873591942969360009710472442595581340
Moler matrix
12
4:
2.294317964090647665607309182114057412461796868058001207936906176670811179465489613041037551303883913
Moler matrix
12
5:
2.336481927683326788799049437329050560190836859190638006235983115679467324234867259348879650476904027
Moler matrix
12
6:
2.403819713802403113336987848025438170001655539504950772770100697551828844457509679567693893326903134
Moler matrix
12
7:
2.514141172494850028830101642439029973154608766973238488607429090602237162666272187748320518971856614
Moler matrix
12
8:
2.706945216556698375779491696267274884968240817112406268592388088568970531904747120235221365404385168
Moler matrix
12
9:
3.084466379985099736029793503701707805256681943346974104826791035396283834282896471523839857465455480
Moler matrix
12
10:
3.986325686054396412600253149569605500426493035557595384270001237042778317831121996234680443361743308
Moler matrix
12
11:
7.199713558917446014073852706595730073107385708930402241059122937069545693794329212024134253647584049
Moler matrix
12
12:
46.95083491321879167725817440009614385395883962647495883872382509649311649470379112849811459761820105
Ris matrix
2
1:
-1.535183758487996431039740422490165315417098857948415404236817685409055649431003481734873027339496906
Ris matrix
2
2:
0.8685170918213297643730737558234986487504321912817487375701510187423889827643368150682063606728302392
Ris matrix
3
1:
-1.505371298751373117664599079911231553522909395280568804077231713689200988609135168131449898038855903
Ris matrix
3
2:
0.8026728391672720862941982989025928725093136595382734501535689597518022146436036668589415547366866085
Ris matrix
3
3:
1.569365126250767698037067447675305347680262402408962020590329420604065440632198167939175009968835961
Ris matrix
4
1:
-1.570745604299979798945478727599881903455484059535179755640491969287641436969384864288603185881084084
Ris matrix
4
2:
-1.481109786131901467429218156356008095728463809888844601762686211646642877201634541932251101269305337
Ris matrix
4
3:
0.7608250983289306071354984653868654141926929077707796557230623658605110685469799043896872571229835379
Ris matrix
4
4:
1.567220768293426849715388894759500775467445437843720892156306291264249436100229978021643220503596359
Ris matrix
5
1:
-1.570636110228254114797845307354377607538679703845401730311873291992906731070552958012497875640181316
Ris matrix
5
2:
-1.460930417456844062667085137510586537964558516543214516295712091492657667984146673108760097156379873
Ris matrix
5
3:
0.7309322466624441191393134913547480559002025214897020676239880915830949534309405759276946931973665627
Ris matrix
5
4:
1.564760296772628792544739514035891302486068854628118689453830026545804577122191198718514412457037412
Ris matrix
5
5:
1.570794619170660186415798074394959707751887479191430410164687900277299789136488491395683787777077850
Ris matrix
6
1:
-1.570796270928807095912059022372407587453646811166158280345929928168244714946280980165931792262062622
Ris matrix
6
2:
-1.570474190411367757972778259678025729052387114712471775097762563827975941645111193084456790991094616
Ris matrix
6
3:
-1.443757268167047635350520814960013100736951630251095557858115357685045678833004885270341142238185332
Ris matrix
6
4:
0.7080460769854204214388283043525881693667819122212000654699037631176599920096746774366724320265346734
Ris matrix
6
5:
1.562180304994812244987144520723239620134897575248895675732645800848597067232675638046762450853482362
Ris matrix
6
6:
1.570789803515445811265373727923074616197294524648085860555246741703465264638035199025750831067313990
Ris matrix
7
1:
-1.570796076356433246031528232983648264270158098375419813962589117292170935354193082858145227205644130
Ris matrix
7
2:
-1.570269162759551703331742315439468616790863453822751661269621697829322912729849857196063214013782266
Ris matrix
7
3:
-1.428859611029969000828667156030418026808558596157164535527139094269581936745848286772700486414758764
Ris matrix
7
4:
0.6897020943345572671226857941242277441748241793936241132867154753092302626881942485749160342435936734
Ris matrix
7
5:
1.559579964119991288179697061604409208189926803933880859593349804188985792808615459228472658094539935
Ris matrix
7
6:
1.570781087625359383547170906662346057710780908152212292529519559619914644333717936872723282731514516
Ris matrix
7
7:
1.570796325000666945963318562997172832414982877810239679970699691207566019620298203085417887185471657
Ris matrix
8
1:
-1.570796326738013648568158890007106257341462677529597551280173139503098780976971136371858906107384324
Ris matrix
8
2:
-1.570795659681313455345676634041416510053311479991771672449161622662258503961898730310596481726397298
Ris matrix
8
3:
-1.570029806688079708014168034610574259831621229943929502119141769459958357986547486947693095118455815
Ris matrix
8
4:
-1.415733263690876452481710696180096722301125122758726868144443649613209526982663203358056120179245797
Ris matrix
8
5:
0.6745123827025735751152401851953129329076918438209120410733789824704647408087421175222601705660082763
Ris matrix
8
6:
1.557010254993787392254224248386505535615486585531596026679508972433298674808020987623793047434592217
Ris matrix
8
7:
1.570768147273065275787170639499784296527518401112672387705248279256781474265316870600518146679005734
Ris matrix
8
8:
1.570796317560902753298811227489636716522555725490890870580515992810026012071732626973678970497609052
Ris matrix
9
1:
-1.570796326464363741145788543538491447531058077948242858049270210288449897699191018273189021917067324
Ris matrix
9
2:
-1.570794949621091296707987090359014005820472190721660948614323723613502453268779127698571605072842175
Ris matrix
9
3:
-1.569763509091327834668202722768138483634123586890268841428665725634827352331288360115706492926276455
Ris matrix
9
4:
-1.404019995522559524406958843363946512816708457702916142614116329689160909643622801353731700121701643
Ris matrix
9
5:
0.6616253958619157918778909543217231381281382618694087758885979260981974681517861966047290699485742968
Ris matrix
9
6:
1.554497287911680774218497041225557844842597222644955731840188365525758506981225161468536220895697968
Ris matrix
9
7:
1.570750954653457812794310584098786598911109567341604934396342147664430265377108019521804494986085346
Ris matrix
9
8:
1.570796299158896534691738739361344267267821555241550324825511476666536110382927032223165729664725258
Ris matrix
9
9:
1.570796326793110457183120776466603456842257778080582115239415792244854882945279322479152866614719741
Ris matrix
10
1:
-1.570796326794840945613295351993454332193195688832167688129700295287308583789483740673454757742030890
Ris matrix
10
2:
-1.570796325696583076166411450328929603721157896093568893038289300411044565896372734389734814761076338
Ris matrix
10
3:
-1.570793890785278153955502852307355418515657443377579563260302798936326467458213089570736451931648448
Ris matrix
10
4:
-1.569476240300454913550395847144881119614127199459176342304432115450551332932703438454307634736781324
Ris matrix
10
5:
-1.393457741202064773970509500782156751009581415354020604606724676988730950704531384613016479435610285
Ris matrix
10
6:
0.6504845350148517612405344005241486994838325546381273287335551466241219781112633407193364046382121505
Ris matrix
10
7:
1.552053841568192776678465612099773769757986947392745224448291507622308226966370634068855659684604854
Ris matrix
10
8:
1.570729652931129702777010382206391856528705529326855226323930496474944728091502479011609943430705086
Ris matrix
10
9:
1.570796263749366591346663434949469624724127727461696674713438079567367831025656064420646370351392116
Ris matrix
10
10:
1.570796326783330478429451856279936839422136391329443966689185816758750936743699023571980619482949643
Ris matrix
11
1:
-1.570796326794499089417303932420917783842894713907220506275742925945342009647104701150568192171502734
Ris matrix
11
2:
-1.570796324049854786277623427460309737879674804720192965960576826190811249201846603421686871666405990
Ris matrix
11
3:
-1.570792443194779270128392928475808411844070933177792713061583428604999290687761683238286322523693670
Ris matrix
11
4:
-1.569172755956649537554446197960014417636784323906084988381573970145414518593983194813896416765205500
Ris matrix
11
5:
-1.383849702743034122196510182875200758868945734886371050028347519103665428515410609560047332687348781
Ris matrix
11
6:
0.6407078235199587249400429964711342886671372786056902679720270040776903990972363648312122499294015934
Ris matrix
11
7:
1.549685347172421504177777090719904629518036420132026508183771409184445895726097731548343220791318890
Ris matrix
11
8:
1.570704475695250970832791794341140775644570697697079819524359815410189802692560322516917068311943569
Ris matrix
11
9:
1.570796205155049160915297038607693924712406509352038925827618171008190351699698428045014877652420342
Ris matrix
11
10:
1.570796326752639722463911191038536085812549556946447792377823518640929476792711492674024435013882508
Ris matrix
11
11:
1.570796326794894894076064922129945459902219588451071199300891939314302389528234346096842044182092254
Ris matrix
12
1:
-1.570796326794896566028782487919207491170896094862025918515650753407994168918405521507325147189598531
Ris matrix
12
2:
-1.570796326793312621449144376212361953907343923091272138428161697330365981922721579041676383335863719
Ris matrix
12
3:
-1.570796321054459527324049213140416496424488555320577281608983397092112729243721018389914356000861223
Ris matrix
12
4:
-1.570790580168271449264756164967750119973628027121665872037951880199012590584282560785708836078275973
Ris matrix
12
5:
-1.568856829646778076500469503294382281147839889555050859984589197852586311221958266944828237298821827
Ris matrix
12
6:
-1.375044680311295259749080730332855797358815397386938180968731862600498281111780910070182253242793581
Ris matrix
12
7:
0.6320227822519383492156156274839911661036021407930858868701549175728328492466206482310130119179605316
Ris matrix
12
8:
1.547393122153019292534679343859198253075564727863518109110863547012147583427526846438118381884357849
Ris matrix
12
9:
1.570675697938604286667330186195170285579287118961806537905359642380864575949514794582949506498658646
Ris matrix
12
10:
1.570796117468700019200967235645951523380630069318999380807170732663462935682739332156428391093064298
Ris matrix
12
11:
1.570796326680035444755799296042184255373462038914089621497404762397902270439023354483569170657767426
Ris matrix
12
12:
1.570796326794883153501586770350461558807655381334121034570100172722887507627882552537079295375329707
second-difference matrix
2
1:
1
second-difference matrix
2
2:
3
second-difference matrix
3
1:
0.5857864376269049511983112757903019214303281246230519268233202620092675215378929611496124656723584273
second-difference matrix
3
2:
2
second-difference matrix
3
3:
3.414213562373095048801688724209698078569671875376948073176679737990732478462107038850387534327641573
second-difference matrix
4
1:
0.3819660112501051517954131656343618822796908201942371378645513772947395371810975502927927958106088625
second-difference matrix
4
2:
1.381966011250105151795413165634361882279690820194237137864551377294739537181097550292792795810608863
second-difference matrix
4
3:
2.618033988749894848204586834365638117720309179805762862135448622705260462818902449707207204189391137
second-difference matrix
4
4:
3.618033988749894848204586834365638117720309179805762862135448622705260462818902449707207204189391137
second-difference matrix
5
1:
0.2679491924311227064725536584941276330571947461896193719441930205480669830911999629188538132427514243
second-difference matrix
5
2:
1
second-difference matrix
5
3:
2
second-difference matrix
5
4:
3
second-difference matrix
5
5:
3.732050807568877293527446341505872366942805253810380628055806979451933016908800037081146186757248576
second-difference matrix
6
1:
0.1980622641951617475277953609851098976681616757362856998928751536011351591441200689972770905629751694
second-difference matrix
6
2:
0.7530203962825329389499902319915203787354505382071957892689011218062926950870254308481149853468292567
second-difference matrix
6
3:
1.554958132087371191422194871006410481067288862470910089376025968205157535942905361850837894783854087
second-difference matrix
6
4:
2.445041867912628808577805128993589518932711137529089910623974031794842464057094638149162105216145913
second-difference matrix
6
5:
3.246979603717467061050009768008479621264549461792804210731098878193707304912974569151885014653170743
second-difference matrix
6
6:
3.801937735804838252472204639014890102331838324263714300107124846398864840855879931002722909437024831
second-difference matrix
7
1:
0.1522409349774264877436336212064234263551667482727150277698045374389299849977952825703201302993108078
second-difference matrix
7
2:
0.5857864376269049511983112757903019214303281246230519268233202620092675215378929611496124656723584273
second-difference matrix
7
3:
1.234633135269820456543080031939202266477310875028745917132398728744907932079820615525972429315432906
second-difference matrix
7
4:
2
second-difference matrix
7
5:
2.765366864730179543456919968060797733522689124971254082867601271255092067920179384474027570684567094
second-difference matrix
7
6:
3.414213562373095048801688724209698078569671875376948073176679737990732478462107038850387534327641573
second-difference matrix
7
7:
3.847759065022573512256366378793576573644833251727284972230195462561070015002204717429679869700689192
second-difference matrix
8
1:
0.1206147584281832318917814453505370601275837314710707338194266744515575780082210821005082203241038651
second-difference matrix
8
2:
0.4679111137620439295952146988891666521283350858392095082919094307156892222862505529435414466389030131
second-difference matrix
8
3:
1
second-difference matrix
8
4:
1.652703644666139302296566746461370407999248645631861225527517243735868355721970529156966773685200852
second-difference matrix
8
5:
2.347296355333860697703433253538629592000751354368138774472482756264131644278029470843033226314799148
second-difference matrix
8
6:
3
second-difference matrix
8
7:
3.532088886237956070404785301110833347871664914160790491708090569284310777713749447056458553361096987
second-difference matrix
8
8:
3.879385241571816768108218554649462939872416268528929266180573325548442421991778917899491779675896135
second-difference matrix
9
1:
0.09788696740969285576712133324123571318860273174849955510538871113969365982961299656241437805837723665
second-difference matrix
9
2:
0.3819660112501051517954131656343618822796908201942371378645513772947395371810975502927927958106088625
second-difference matrix
9
3:
0.8244294954150537416625880907218544628046951247137080178554550384854430516752960849829919002745173281
second-difference matrix
9
4:
1.381966011250105151795413165634361882279690820194237137864551377294739537181097550292792795810608863
second-difference matrix
9
5:
2
second-difference matrix
9
6:
2.618033988749894848204586834365638117720309179805762862135448622705260462818902449707207204189391137
second-difference matrix
9
7:
3.175570504584946258337411909278145537195304875286291982144544961514556948324703915017008099725482672
second-difference matrix
9
8:
3.618033988749894848204586834365638117720309179805762862135448622705260462818902449707207204189391137
second-difference matrix
9
9:
3.902113032590307144232878666758764286811397268251500444894611288860306340170387003437585621941622763
second-difference matrix
10
1:
0.08101405277100522021926388586734460187509030315567608991100988200961938340742666605899143865278552814
second-difference matrix
10
2:
0.3174929343376376622763767021612645649734150031589242027146997646366977861967154535138269546604290767
second-difference matrix
10
3:
0.6902785321094298718861498550674128936324176013261431447874087909882098201012902158156582064230603398
second-difference matrix
10
4:
1.169169973996227148941451701540753592951990179070926375147553335243120438110254020557257716168071553
second-difference matrix
10
5:
1.715370323453429719112414662767260662417897277748031343163834426881989020798252592196435025752654762
second-difference matrix
10
6:
2.284629676546570280887585337232739337582102722251968656836165573118010979201747407803564974247345238
second-difference matrix
10
7:
2.830830026003772851058548298459246407048009820929073624852446664756879561889745979442742283831928447
second-difference matrix
10
8:
3.309721467890570128113850144932587106367582398673856855212591209011790179898709784184341793576939660
second-difference matrix
10
9:
3.682507065662362337723623297838735435026584996841075797285300235363302213803284546486173045339570923
second-difference matrix
10
10:
3.918985947228994779780736114132655398124909696844323910088990117990380616592573333941008561347214472
second-difference matrix
11
1:
0.06814834742186342650051360054220526473219032198319089919531384737915357204028896730487651628385909622
second-difference matrix
11
2:
0.2679491924311227064725536584941276330571947461896193719441930205480669830911999629188538132427514243
second-difference matrix
11
3:
0.5857864376269049511983112757903019214303281246230519268233202620092675215378929611496124656723584273
second-difference matrix
11
4:
1
second-difference matrix
11
5:
1.482361909794958475302202324751903343301862197360138972371993585369886050502396006155264050611500669
second-difference matrix
11
6:
2
second-difference matrix
11
7:
2.517638090205041524697797675248096656698137802639861027628006414630113949497603993844735949388499331
second-difference matrix
11
8:
3
second-difference matrix
11
9:
3.414213562373095048801688724209698078569671875376948073176679737990732478462107038850387534327641573
second-difference matrix
11
10:
3.732050807568877293527446341505872366942805253810380628055806979451933016908800037081146186757248576
second-difference matrix
11
11:
3.931851652578136573499486399457794735267809678016809100804686152620846427959711032695123483716140904
second-difference matrix
12
1:
0.05811636514789594568603544741242154550026978852199282282471094704591658247998664613485078718323147689
second-difference matrix
12
2:
0.2290879486935802081992489559698022427890031673049301963951923825464848859325442749322354041735050528
second-difference matrix
12
3:
0.5029785036577978027307388005972972323070968196483477318607375217053365852911263478121111720050348341
second-difference matrix
12
4:
0.8638705065376883949763848817449667509330148950929636610406749968648366419176182165492715001975116698
second-difference matrix
12
5:
1.290790225914928748060724214799963051367289135772410493156521262626479200044929103303040248892670184
second-difference matrix
12
6:
1.758926639489353893301864625094912835452637681544857190406102351966410839965879605768495303709919772
second-difference matrix
12
7:
2.241073360510646106698135374905087164547362318455142809593897648033589160034120394231504696290080228
second-difference matrix
12
8:
2.709209774085071251939275785200036948632710864227589506843478737373520799955070896696959751107329816
second-difference matrix
12
9:
3.136129493462311605023615118255033249066985104907036338959325003135163358082381783450728499802488330
second-difference matrix
12
10:
3.497021496342202197269261199402702767692903180351652268139262478294663414708873652187888827994965166
second-difference matrix
12
11:
3.770912051306419791800751044030197757210996832695069803604807617453515114067455725067764595826494947
second-difference matrix
12
12:
3.941883634852104054313964552587578454499730211478007177175289052954083417520013353865149212816768523
Definition
For a named symmetric classical test matrix $A_n$, this table gives the $k$th eigenvalue $\lambda_k(A_n)$ [1], ordered increasingly, where $n$ is the order of the matrix and $1\leq k\leq n$.
Parameters
$A_n$
—   matrix family (one of the real symmetric matrix families from MATLAB's gallery [5] or the Test Matrix Toolbox source [6])
$n$
—   order ($n\geq 1$)
$k$
—   eigenvalue index ($1\leq k\leq n$)
Formulas
(1)
For the second-difference matrix, $\lambda_k=2-2\cos(k\pi/(n+1))$ for $k=1,\ldots,n$.
(2)
For the Minij matrix, $\lambda_k=\dfrac{1}{4}\sec^2\!\left(\dfrac{k\pi}{2n+1}\right)$ for $k=1,\ldots,n$.
(3)
The eigenvalues of the symmetric Pascal matrix occur in reciprocal pairs; when $n$ is odd, $1$ is an eigenvalue.
Comments
(4)
Indices are $1$-based. The matrices are $A_{ij}=1/(i+j-1)$ for the Hilbert matrix [2]; $A_{ij}=\min(i,j)/\max(i,j)$ for the Lehmer matrix [3]; $A_{ij}=\binom{i+j-2}{i-1}$ for the symmetric Pascal matrix [4]; $A_{ij}=1/(i+j)$ for the Cauchy matrix, the scalar default case of gallery("cauchy",n) [5]; $A_{ij}=|i-j|$ for the Fiedler matrix; $A_{ij}=2^{-|i-j|}$ for the Kac-Murdock-Szegő matrix; and $A_{ij}=\min(i,j)$ for the Minij matrix.
(5)
The Wilkinson, Moler and Ris matrices use the definitions in the Test Matrix Toolbox source [6]. The Wilkinson matrix is symmetric tridiagonal with off-diagonal entries $1$ and diagonal entries $|(n-1)/2-(i-1)|$. The Moler matrix has $A_{ii}=i$ and $A_{ij}=\min(i,j)-2$ for $i\neq j$. The Ris matrix, also called the Dingdong matrix, is $A_{ij}=(1/2)/(n-i-j+3/2)$. The second-difference matrix is tridiagonal with diagonal entries $2$ and off-diagonal entries $-1$.
(6)
This table includes the real symmetric matrix families from MATLAB's gallery [5] and the Test Matrix Toolbox source [6]. Nonsymmetric families from those collections are not rows. The Clement matrix is also not included: the default Clement form is nonsymmetric, and the symmetric Clement form is diagonally similar to the default form and has the integer eigenvalues $\pm(n-1),\pm(n-3),\ldots$, with $0$ when $n$ is odd.
(7)
For every listed order, only the Fiedler, Ris and Wilkinson spectra contain negative eigenvalues. The Fiedler spectrum has $n-1$ negative eigenvalues, the Ris spectrum has $\lfloor n/2\rfloor$, and the Wilkinson spectrum has one.
Programs
(P1)
Sage
import numberdb.sage
from sage.matrix.constructor import matrix
from sage.rings.qqbar import AA, _init_qqbar
from sage.rings.rational_field import QQ

_init_qqbar()
A = matrix(QQ, 3, 3, lambda i, j: QQ(1) / QQ(i + j + 1))
sorted(AA(root) for root in A.charpoly().roots(
    ring=AA, multiplicities=False))
Links
Similar tables
Condition numbers of the classical test matrices —   stores the 2-norm condition numbers of the same gallery matrix families
$\cos(\pi x)$ for rational $x$ —   the Minij and second-difference spectra are elementary functions of cosine values at rational arguments
Characteristic polynomials of connected graphs —   stores exact characteristic polynomials of symmetric integer adjacency matrices rather than numerical eigenvalues
Data properties
Entries are of type: real number
Table is complete: no (it holds every eigenvalue for the listed symmetric matrix families with $2\leq n\leq12$, giving the nontrivial small orders while keeping this table to 847 eigenvalues)
How they were obtained:

The generator builds each matrix over $\mathbb{Q}$, computes its characteristic polynomial exactly, isolates its roots in Sage's algebraic real field, orders those algebraic roots increasingly, returns roots proved rational as exact rationals, and returns the other roots as real balls with 96 guard bits beyond the 100 digits written.

more

During generation it checks that every listed characteristic polynomial has $n$ real roots, that the eigenvalue sum equals the trace, that the eigenvalue product equals the determinant, that the Minij and second-difference rows agree with the closed forms in (2) and (1), and that the symmetric Pascal eigenvalues occur in reciprocal pairs.