Nonsingularity and group invertibility of linear combinations of two k-potent matrices

Abstract

An n×n complex matrix A is said to be k-potent if Ak=A. Let T1 and T2 be k-potent and c1 and c2 be two nonzero complex numbers. We study the range space, null space, nonsingularity and group invertibility of linear combinations T=c1T1+c2T2 of two k-potent matrices T1 and T2. © 2010 Taylor & Francis.