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- Fiedler matrix - Kac-Murdock-Szego matrix+- Kac-Murdock-Szegő matrix - Minij matrix - Grcar matrix
title: matrix family display: $A_n$- constraints: one of the named matrix families listed in the comments+ constraints: one of the classical test matrix families named here, with definitions+ from the cited references, including MATLAB's `gallery` documentation CITE{MathWorksGallery}+ and the Test Matrix Toolbox source CITE{TMTGallery} values: hilbert: Hilbert matrix
formula-second-difference: For the second-difference matrix, the characteristic polynomials satisfy $p_0(x)=1$, $p_1(x)=x-2$, and $p_n(x)=(x-2)p_{n-1}(x)-p_{n-2}(x)$.- formula-redheffer: For the Redheffer matrix, $\chi_{A_n}(0)=(-1)^n M(n)$, where- $M(n)$ is the Mertens function.+ Equivalently, $p_n(x)=U_n((x-2)/2)$, where $U_n$ is the HREF{Chebyshev_polynomials_of_the_second_kind}[Chebyshev+ polynomial of the second kind].+ formula-redheffer: For the Redheffer matrix CITE{WikiRedheffer}, $\chi_{A_n}(0)=(-1)^n+ M(n)$, where $M(n)$ is the Mertens function. Programs: program-sage:
from sage.rings.rational_field import QQ ++ # Hilbert matrix, n = 3. A = matrix(QQ, 3, 3, lambda i, j: QQ(1) / QQ(i + j + 1))
- algebraic - eigenvalue+- polynomial Data properties: type: Q[]
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