On the Yang-Baxter-like Matrix Equation for Rank-two Matrices
Let A = PQT, where P and Q are two n × 2 complex matrices of full column rank such that QTP is singular. We solve the quadratic matrix equation AXA = XAX. Together with a previous paper devoted to the case that QTP is nonsingular, we have completely solved the matrix equation with any given matrix A of rank-two.
(2017). On the Yang-Baxter-like Matrix Equation for Rank-two Matrices. Open Mathematics, 15, 340-353.
Available at: https://aquila.usm.edu/fac_pubs/17709