Exact rational solution of the matrix equation \(A=p(X)\) by linearization

DOI10.1016/j.laa.2007.05.030zbMath1131.15013OpenAlexW2026021456MaRDI QIDQ996307

Michael P. Drazin

Publication date: 14 September 2007

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2007.05.030

zbMATH Keywords

exact solutionsinfinite matricesDiophantine equations

Mathematics Subject Classification ID

Matrix equations and identities (15A24) Polynomials in number theory (11C08) Matrices, determinants in number theory (11C20)

Related Items (2)

How to solve the matrix equation \(XA-AX=f(X)\) ⋮ Solutions of the matrix equation \(p(X)=A\), with polynomial function \(p(\lambda)\) over field extensions of \(\mathbb{Q}\)

Cites Work

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• Computing real square roots of a real matrix
• Universal properties of infinite matrices
• The moment and Gram matrices, distinct eigenvalues and zeroes, and rational criteria for diagonalizability
• On the Square Roots of Infinite Matrices
• On the Canonical Form of a Rational Integral Function of a Matrix
• Square roots of complex matrices

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