Some bounds for determinants of relatively $D$-stable matrices
Spectral Theory
2022-05-24 v1
Abstract
In this paper, we study the class of relatively -stable matrices and provide the conditions, sufficient for relative -stability. We generalize the well-known Hadamard inequality, to provide upper bounds for the determinants of relatively -stable and relatively additive -stable matrices. For some classes of -stable matrices, we estimate the sector gap between matrix spectra and the imaginary axis. We apply the developed technique to obtain upper bounds for determinants of some classes of -stable matrices, e.g. diagonally stable, diagonally dominant and matrices with -scalings.
Cite
@article{arxiv.2205.10823,
title = {Some bounds for determinants of relatively $D$-stable matrices},
author = {Olga Y. Kushel},
journal= {arXiv preprint arXiv:2205.10823},
year = {2022}
}