English

Anti-commuting Solutions of the Yang-Baxter-like Matrix Equation

Numerical Analysis 2025-11-10 v1 Numerical Analysis Rings and Algebras Exactly Solvable and Integrable Systems

Abstract

We solve the Yang-Baxter-like matrix equation AXA=XAXAXA = XAX for a general given matrix AA to get all anti-commuting solutions, by using the Jordan canonical form of AA and applying some new facts on a general homogeneous Sylvester equation. Our main result provides all the anti-commuting solutions of the nonlinear matrix equation.

Keywords

Cite

@article{arxiv.2511.05088,
  title  = {Anti-commuting Solutions of the Yang-Baxter-like Matrix Equation},
  author = {Mohammed Ahmed Adam Abdalrahman and Huijian Zhu and Jiu Ding and Qianglian Huang},
  journal= {arXiv preprint arXiv:2511.05088},
  year   = {2025}
}