Nonsingularity and group invertibility of linear combinations of two k -potent matrices
Julio Benítez, Xiaoji Liu, Tongping Zhu · Linear and Multilinear Algebra · 2010
An n × n complex matrix A is said to be k-potent if A k = A. Let T 1 and T 2 be k-potent and c 1 and c 2 be two nonzero complex numbers. We study the range space, null space, nonsingularity and group invertibility of linear combinations T = c 1 T 1 + c 2 T 2 of two k-potent matrices T 1 and T 2.