$\sigma$-Stable Matrices

Michael Thorne

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arXiv · 2012.04601

$\sigma$-Stable Matrices

Michael Thorne

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Abstract

$\sigma$-Stable matrices are introduced and it is shown that the real roots of the polynomials comprising the coefficients of the characteristic polynomial indicate the coefficient sign changes. A proof of Obrechkoff is then used to show that the largest real root from the coefficients is the point of stability when the maximal eigenvalue of the $\sigma$-stable matrix is in $\mathbb{R}$. Some implications of the coefficient behaviour for a scaling relation are then discussed.

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Michael Thorne. 2020-11-30. $\sigma$-Stable Matrices. https://arxiv.org/abs/2012.04601

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