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

In this paper, {K,s+1}-potent matrices are considered. A matrix A∈Cn×n is called {K,s+1}-potent when KAs+1K=A where K is an involutory matrix and s∈{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∈Cn×n (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.