Complete Commuting Solutions of the Yang-Baxter-like Matrix Equation for Diagonalizable Matrices
Document Type
Article
Publication Date
7-2016
Department
Mathematics
Abstract
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.
Publication Title
Computers and Mathematics with Applications
Volume
72
Issue
1
First Page
194
Last Page
201
Recommended Citation
Dong, Q.,
Ding, J.
(2016). Complete Commuting Solutions of the Yang-Baxter-like Matrix Equation for Diagonalizable Matrices. Computers and Mathematics with Applications, 72(1), 194-201.
Available at: https://aquila.usm.edu/fac_pubs/17457