Solving the Yang-Baxter-Like Matrix Equation With Non-Diagonalizable Elementary Matrices
Let A = I − uvt, where u and v are two n-dimensional complex vectors with vtu = 0. Thus A is not diagonalizable. We find all solutions of the quadratic matrix equation AXA = XAX. This is a continuation of the work [Compters Math. Appl., 72(6):1541-1548, 2016] from the case of diagonalizable elementary matrices to non-diagonalizable ones.