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arXiv · 2109.01563

Perturbing eigenvalues of nonnegative centrosymmetric matrices

Roberto C. Díaz·Ana I. Julio·Yankis R. Linares
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Abstract

An $n\times n$ matrix $C$ is said to be {\it centrosymmetric} if it satisfies the relation $JCJ=C$, where $J$ is the $n\times n$ 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 $n\times n$ nonnegative centrosymmetric matrix without changing any of the remaining eigenvalues neither nonnegativity nor the centrosymmetric structure. Moreover, our results allow partially answer some known questions given by Guo [11] and by Guo and Guo [12]. Our proofs generate algorithmic procedures that allow to compute a solution matrix.

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Roberto C. Díaz, Ana I. Julio, Yankis R. Linares. 2021-07-23. Perturbing eigenvalues of nonnegative centrosymmetric matrices. https://arxiv.org/abs/2109.01563

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