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

Published 7 Nov 2025 in math.NA, cs.NA, math.RA, and nlin.SI | (2511.05088v1)

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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