Complete Commuting Solutions of the Yang-Baxter-like Matrix Equation for Diagonalizable Matrices
Let A be a square matrix that is diagonalizable. We find all the commuting solutions of the quadratic matrix equation AXA = XAX, by taking advantage of the Jordan form structure of A, together with the help of a well-known theorem on the uniqueness of a solution to Sylvester's equation. Two special classes of the given matrix A are further investigated, including circular matrices and those that are equal to some of their powers. Moreover, all the non commuting solutions are constructed when A is a Householder matrix, based on a spectral perturbation result. (C) 2016 Elsevier Ltd. All rights reserved.
Computers and Mathematics with Applications
(2016). Complete Commuting Solutions of the Yang-Baxter-like Matrix Equation for Diagonalizable Matrices. Computers and Mathematics with Applications, 72(1), 194-201.
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