Some bounds for determinants of relatively $D$-stable matrices

Olga Y. Kushel

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arXiv · 2205.10823

Some bounds for determinants of relatively $D$-stable matrices

Olga Y. Kushel

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Abstract

In this paper, we study the class of relatively $D$-stable matrices and provide the conditions, sufficient for relative $D$-stability. We generalize the well-known Hadamard inequality, to provide upper bounds for the determinants of relatively $D$-stable and relatively additive $D$-stable matrices. For some classes of $D$-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 $D$-stable matrices, e.g. diagonally stable, diagonally dominant and matrices with $Q^2$-scalings.

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BibTeX RIS

Olga Y. Kushel. 2022-05-22. Some bounds for determinants of relatively $D$-stable matrices. https://arxiv.org/abs/2205.10823

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