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