Relations between {K, s + 1}-potent matrices and different classes of complexmatrices

Abstract

In this paper, {K, s + 1}-potent matrices are considered. A matrix A in C{nxn} is called {K, s + 1}-potent when KA^(s+1)K = A where K is an involutory matrix and s in {1, 2, 3, . . .}. Specifically, {K, s + 1}-potent matrices are analyzed considering their relations to different classes of complex matrices. These classes of matrices are: {s + 1}-generalized projectors, {K}-Hermitian matrices, normal matrices, and matrices B ¿in C{nxn} (anti-)commuting with K or such that KB is involutory, Hermitian or normal. In addition, some new relations for K-generalized centrosymmetric matrices have been derived.