All Solutions of the Yang–Baxter-Like Matrix Equation for Nilpotent Matrices of Index Two. (18th June 2020) - Zhou, Duanmei; Ding, Jiawen
Abstract : Let A be a nilpotent matrix of index two, and consider the Yang–Baxter-like matrix equation A X A = X A X . We first obtain a system of matrix equations of smaller sizes to find all the solutions of the original matrix equation. When A is a nilpotent matrix with rank 1 and rank 2, we get all solutions of the Yang–Baxter-like matrix equation.