Spectrally and inertially arbitrary sign patterns
type: Item
instance of: scholarly article
title: Spectrally and inertially arbitrary sign patterns
zbMATH Open document ID: 1065.15009
author: M. Cavers
author: Kevin N. Vander Meulen
published in: Linear Algebra and its Applications
publication date: 2005-02-23T00:00:00Z
review text: This paper gives sign patterns generalizing those of \textit{Y. Gao} and \textit{Y. Shao} [Linear Multilinear Algebra 49, No. 2, 161-168 (2001; Zbl 0993.15009)], and of \textit{Z. Miao} and \textit{J. Li} [Linear Algebra Appl. 357, No. 1--3, 133--141 (2002; Zbl 1015.05019)], which are spectrally arbitrary, that is, an \(n\times n\) matrix with one of these sign patterns can have any multiset of \(n\) complex numbers which is conjugation invariant, as its spectrum. It characterizes \(3\times 3\) spectrally arbitrary and inertially arbitrary sign patterns.
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 05C20
zbMATH DE Number: 2137772
zbMATH Keywords: sign pattern
zbMATH Keywords: inertia
zbMATH Keywords: spectrum
zbMATH Keywords: nilpotent
zbMATH Keywords: potentially stable
reviewed by: Ki Hang Kim
MaRDI profile type: Publication
full work available at URL: j.laa.2004.06.003
OpenAlex ID: W2098334461
cites work: Minimal Spectrally Arbitrary Sign Patterns
cites work: Spectrally arbitrary patterns
cites work: On the spectra of close-to-Schwarz matrices
cites work: Low rank perturbations and the spectrum of a tridiagonal sign pattern.
cites work: Potentially nilpotent sign pattern matrices
cites work: Inertially arbitrary patterns
cites work: Sign-patterns which require a positive eigenvalue
cites work: On the Spectra of Striped Sign Patterns
cites work: Inertially arbitrary (\(2r-1\))-diagonal sign patterns
cites work: Sign pattern matrices that allow a nilpotent matrix
DOI: 10.1016/J.LAA.2004.06.003
description: scientific article; zbMATH DE number 2137772