{k}-Group Periodic Matrices

In this paper we deal with two problems related to {k}-group periodic matrices (i.e., A# = Aᵏ⁻¹, where A# is the group inverse of a matrix A). First, we give different characterizations of {k}-group periodic matrices. Later, we present characterizations of the {k}-group periodic matrices for linear combinations of projectors. This work extends some well-known results in the literature.