Perturbing eigenvalues of nonnegative centrosymmetric matrices

Abstract

An matrix C is said to be centrosymmetric if it satisfies the relation JCJ = C, where J is the counteridentity matrix. Centrosymmetric matrices have a rich eigenstructure that has been studied extensively in the literature. Many results for centrosymmetric matrices have been generalized to wider classes of matrices that arise in a wide variety of disciplines. In this paper, we obtain interesting spectral properties for nonnegative centrosymmetric matrices. We show how to change one single eigenvalue, two or three eigenvalues of an nonnegative centrosymmetric matrix without changing any of the remaining eigenvalues, the nonnegativity, or the centrosymmetric structure. Moreover, our results allow partially answer some known questions given by [Guo W. Eigenvalues of nonnegative matrices. Linear Algebra Appl. 266;1997:261–270] and by [Guo S, Guo W. Perturbing non-real eigenvalues of non-negative real matrices. Linear Algebra Appl. 426;2007:199–203]. Our proofs generate algorithmic procedures that allow one to compute a solution matrix.