Inertially arbitrary sign patterns with no nilpotent realization
type: Item
instance of: scholarly article
title: Inertially arbitrary sign patterns with no nilpotent realization
zbMATH Open document ID: 1121.15015
author: In-Jae Kim
author: D. D. Olesky
author: P. van den Driessche
published in: Linear Algebra and its Applications
publication date: 2007-03-09T00:00:00Z
review text: A family of irreducible sign patterns \(G_{2k+1}\;(k\geq 2)\) is defined and is proved to be initially arbitrary, but not potentially nilpotent; a proof is based on certain realizations, the nilpotent Jacobi method not being available. The paper also derives properties of coefficients of characteristic polynomials with certain fixed inertias. This is used to prove that \(G_5\) and \(G_7\) are minimal arbitrary sign patterns.
reviewed by: Erwin O. Kreyszig
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 15A29
zbMATH DE Number: 5132596
zbMATH Keywords: inertially arbitrary pattern
zbMATH Keywords: potentially nilpotent
zbMATH Keywords: spectrally arbitrary pattern
zbMATH Keywords: irreducible sign patterns
zbMATH Keywords: nilpotent Jacobi method
MaRDI profile type: Publication
full work available at URL: j.laa.2006.07.010
OpenAlex ID: W2017033823
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DOI: 10.1016/J.LAA.2006.07.010
description: scientific article; zbMATH DE number 5132596