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

2025/11/07 by Abdalrahman, Mohammed Ahmed Adam, Zhu, Huijian, Ding, Jiu +1
Computer Science · Mathematics · #15A18 #15A24 #Advanced Optimization Algorithms Research #Advanced Topics in Algebra #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2511.05088

openalex publication_date 2025/11/07 · openalex created_date 2025/11/11 · openalex updated_date 2026/07/28

Abstract

We solve the Yang-Baxter-like matrix equation AXA = XAX for a general given matrix A to get all anti-commuting solutions, by using the Jordan canonical form of A 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.

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