Resumo: In this talk, we deal with {K;s+1}-potent matrices. These matrices generalize all the following classes of matrices: k-potent matrices, periodic matrices, idempotent matrices, involutory matrices, centrosymmetric matrices, mirrorsymetric matrices, circulant matrices, etc. Several applications of these classes of matrices can be found in the literature. In this talk, we study different properties of {K; s + 1}-potent matrices. Some characterizations of this kind of matrices will be presented: from a spectral point of view, in terms of powers of the matrix, by means of the group inverse and, via a block representation of a matrix of index 1. Then, two applications will be presented.