Further results on generalized centro-invertible matrices

Abstract

This paper deals with generalized centro-invertible matrices introduced by the authors in [Generalized centro-invertible matrices with applications, Applied Mathematics Letters, 38, 106-109, 2014]. As a first result, we state the coordinability between the classes of involutory matrices, generalized centro-invertible matrices, and {K}-centrosymmetric matrices. Then, some characterizations of generalized centro-invertible matrices are obtained. A spectral study of generalized centro-invertible matrices is given. In addition, we prove that the sign of a generalized centro-invertible matrix is {K}-centrosymmetric and that the class of generalized centro-invertible matrices is closed under the matrix sign function. Finally, some algorithms have been developed for the construction of generalized centro-invertible matrices.