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 for a general given matrix to get all anti-commuting solutions, by using the Jordan canonical form of 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}
}