Positivity of principal minors, sign symmetry and stability.
type: Item
instance of: scholarly article
title: Positivity of principal minors, sign symmetry and stability.
zbMATH Open document ID: 1044.15012
DOI: 10.1016/S0024-3795(02)00547-5
author: Daniel Hershkowitz
author: Nathan Keller
published in: Linear Algebra and its Applications
publication date: 2003-05-04T00:00:00Z
review text: The authors study the relation between positivity of principal minors, sign symmetry and stability of matrices. In Section 1 they give many definitions of terminologies used in this paper. In Section 2 they show that for sign symmetric matrices positivity of principal minors and stability are equivalent. In Section 3, for \(3\times 3\) matrices they generalize the results of the previous section. This result does not hold in general for matrices of any oder \(n\). In Section 4 they study matrices whose scalings have \(P_0\)-matrix square. In Section 5 they consider the relation between the spectra of \(P^S\)-matrices and \(Q^S\)-matrices. Finally, they refer to the relation between \(P^S\)-matrices or \(Q^S\)-matrices and stability, concentrating on \(P^2\)-matrices. They give many open questions.
Mathematics Subject Classification ID: 15B48
Mathematics Subject Classification ID: 15A18
zbMATH DE Number: 1903580
zbMATH Keywords: \(P\)-matrix
zbMATH Keywords: \(Q\)-matrix
zbMATH Keywords: Sign symmetric matrix
zbMATH Keywords: Weakly sign symmetric matrix
zbMATH Keywords: Stable matrix
zbMATH Keywords: Semistable matrix
zbMATH Keywords: \(P\)-matrix powers
zbMATH Keywords: \(D\)-stability
reviewed by: Takayuki Nôno
MaRDI profile type: Publication
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full work available at URL: s0024-3795(02)00547-5
OpenAlex ID: W2091228839
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description: scientific article; zbMATH DE number 1903580