On nonsingularity of combinations of two group invertible matrices and two tripotent matrices

Benítez López Julio, XIAOJI LIU, Wu Shuxia

2011

Linear and Multilinear Algebra

Let T 1 and T 2 be two n × n tripotent matrices and c 1, c 2 two nonzero complex numbers. We mainly study the nonsingularity of combinations T = c 1T 1 + c 2T 2 - c 3T 1T 2 of two tripotent matrices T 1 and T 2, and give some formulae for the inverse of c 1T 1 + c 2T 2 - c 3T 1T 2 under some conditions. Some of these results are given in terms of group invertible matrices. © 2011 Copyright Taylor and Francis Group, LLC.