The matrix equation XA-AX=f(X) when A is diagonalizable

2014/07/31 by Gérald Bourgeois, Bourgeois, Gerald
Mathematics · #15A24 #Advanced Differential Equations and Dynamical Systems #Advanced Topics in Algebra #FOS: Mathematics #Meromorphic and Entire Functions #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1407.8468

openalex publication_date 2014/07/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

K is an algebraically closed field with characteristic 0 and f is a polynomial or a holomorphic function. We study all solutions of the equation XA-AX=f(X), in the unknown X∈ M_n(K), when A∈ M_n(K) is diagonalizable.

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