Various symmetries in matrix theory with application to modeling dynamic systems

Abstract

In this paper, we recall centrally symmetric matrices and introduce some new kinds of symmetric matrices such as row-wise symmetric matrices, column-wise symmetric matrices, and plus symmetric matrices. The relations between these kinds of matrices are also presented. Furthermore, a useful result is obtained about the types of the eigenvectors of centrally symmetric matrices leading to a limit-wise relation between centrally symmetric matrices and plus symmetric matrices which can be applied to mathematical modeling of dynamical systems in engineering applications.