1. Perturbing eigenvalues of nonnegative centrosymmetric matrices
- Author
-
Díaz, Roberto C., Julio, Ana I., and Linares, Yankis R.
- Subjects
Algebra and Number Theory ,Computer Science::Computational Engineering, Finance, and Science ,FOS: Mathematics ,Mathematics - Combinatorics ,Physics::Optics ,Combinatorics (math.CO) - 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., Comment: 23 pages
- Published
- 2022