All Solutions of the Yang-Baxter-like Matrix Equation When $A^3 = A$

Mansour  Saeed Ibrahim Adam; Jiu  Ding; Qianglian  Huang; Lanping  Zhu

Volume 9, Number 3, 2019, Pages 1022-1031 DOI：10.11948/2156-907X.20180244

All Solutions of the Yang-Baxter-like Matrix Equation When $A^3 = A$

Mansour Saeed Ibrahim Adam,Jiu Ding,Qianglian Huang,Lanping Zhu

Keywords:Yang-Baxter-like matrix equation, diagonalizable matrix, eigenvalue.

Abstract:

Let $A$ be a square matrix satisfying $A^3 = A$. We find all solutions of the Yang-Baxter matrix equation $AXA=XAX$, based on our previous result on all the solutions of the same equation for a matrix $A$ such that $A^2 = I$.

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