Perturbing eigenvalues of nonnegative centrosymmetric matrices

An n x n matrix C is said to be centrosymmetric if it satisfies the relation JCJ = C, where J is the n x n 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 n x n 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.