Computing Solutions of the Yang-Baxter-Like Matrix Equation for Diagonalisable Matrices

Abstract

The Yang-Baxter-like matrix equation $AXA = XAX$ is reconsidered, where $A$ is any complex square matrix. A collection of spectral solutions for the unknown square matrix $X$ were previously found. When $A$ is diagonalisable, by applying the mean ergodic theorem we propose numerical methods to calculate those solutions.