Some Rank Formulas for the Yang-Baxter Matrix Equation AXA = XAX
Lifang Dai, Maolin Liang, Yonghong Shen · Wuhan University Journal of Natural Sciences · 2021
Let A be an arbitrary square matrix, then equation AXA =XAX with unknown X is called Yang-Baxter matrix equation. It is difficult to find all the solutions of this equation for any given A. In this paper, the relations between the matrices A and B are established via solving the associated rank optimization problem, where B =AXA = XAX, and some analytical formulas are derived, which may be useful for finding all the solutions and analyzing the structures of the solutions of the above Yang-Baxter matrix equation.