SOLVING THE YANG-BAXTER-LIKE MATRIX EQUATION WITH NON-DIAGONALIZABLE ELEMENTARY MATRICES

摘要

Let A = I -uv(T), where u and v are two n-dimensional complex vectors with v(T) u=0. Thus A is not diagonalizable. We find all solutions of the quadratic matrix equation AXA=XAX. This is a continuation of the work [Computers Math. Appl., 72(6):1541-1548, 2016] from the case of diagonalizable elementary matrices to non-diagonalizable ones.