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Perturbing eigenvalues of nonnegative centrosymmetric matrices.
- Source :
-
Linear & Multilinear Algebra . 2023, Vol. 71 Issue 16, p2670-2685. 16p. - Publication Year :
- 2023
-
Abstract
- An n × n matrix C is said to be centrosymmetric if it satisfies the relation JCJ = C, where J is the n × 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 × 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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 03081087
- Volume :
- 71
- Issue :
- 16
- Database :
- Academic Search Index
- Journal :
- Linear & Multilinear Algebra
- Publication Type :
- Academic Journal
- Accession number :
- 173436041
- Full Text :
- https://doi.org/10.1080/03081087.2022.2118214