On the Commuting Solutions to the Yang-Baxter-like Matrix Equation for Identity Matrix Minus Special Rank-two Matrices⋆
Hui-Hui Yin, Xiang Wang, Xiao-Bin Tang, Lei Chen
Let A = I − PQT, where P and Q are two n × 2 complex matrices of full column rank such that det(QTP) = 0. We find all the commuting solutions of the quadratic matrix equation AXA = XAX.