Anti-commuting Solutions of the Yang-Baxter-like Matrix Equation
Mohammed Ahmed Adam Abdalrahman, Huijian Zhu, Jiu Ding, Qianglian Huang

TL;DR
This paper characterizes all anti-commuting solutions to a nonlinear matrix equation similar to the Yang-Baxter equation by leveraging Jordan canonical forms and Sylvester equation properties.
Contribution
It provides a complete characterization of anti-commuting solutions to the Yang-Baxter-like matrix equation using novel methods involving Jordan forms and Sylvester equations.
Findings
All anti-commuting solutions are explicitly characterized.
The solutions depend on the Jordan canonical form of A.
The approach introduces new insights into solving nonlinear matrix equations.
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.
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Taxonomy
TopicsMatrix Theory and Algorithms · Advanced Topics in Algebra · Advanced Optimization Algorithms Research
