English

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 DD-stable matrices and provide the conditions, sufficient for relative DD-stability. We generalize the well-known Hadamard inequality, to provide upper bounds for the determinants of relatively DD-stable and relatively additive DD-stable matrices. For some classes of DD-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 DD-stable matrices, e.g. diagonally stable, diagonally dominant and matrices with Q2Q^2-scalings.

Keywords

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}
}
R2 v1 2026-06-24T11:24:44.733Z