Interlacing properties of the eigenvalues of some matrix classes
Spectral Theory
2012-12-07 v1 Rings and Algebras
Abstract
We establish the eigenvalue interlacing property (i.e. the smallest real eigenvalue of a matrix is less than the smallest real eigenvalue of any its principal submatrix) for the class of matrices, introduced by Kotelyansky (all principal and all almost principal minors of these matrices are positive). We show that certain generalizations of Kotelyansky and totally positive matrices also possess this property. We prove some interlacing inequalities for the other eigenvalues of Kotelyansky matrices.
Cite
@article{arxiv.1212.1387,
title = {Interlacing properties of the eigenvalues of some matrix classes},
author = {Olga Y. Kushel},
journal= {arXiv preprint arXiv:1212.1387},
year = {2012}
}
Comments
23 pages