On the invariance of the sign pattern of matrix eigenvectors under perturbation
type: Item
instance of: scholarly article
title: On the invariance of the sign pattern of matrix eigenvectors under perturbation
zbMATH Open document ID: 0797.15015
DOI: 10.1016/0024-3795(94)90315-8
author: V. Pereyra
published in: Linear Algebra and its Applications
publication date: 1994-10-24T00:00:00Z
review text: The authors investigate two problems concerning a real regular matrix \(A\) with simple eigenvalue \(\lambda_ i\) and corresponding eigenvector \(x^ i\). Moreover, let \(\delta A\) be a real perturbation of \(A\). Firstly, if \(\delta A\) is satisfying certain explicitly given bounds then the eigenvector \(\widetilde x^ i\) of \(A+\delta A\) will have the same sign pattern as \(x^ i\). Secondly, given a real interval \(I\) with midpoint \(\lambda_ i\) then conditions on \(\delta A\) are stated ensuring that the eigenvalue \(\widetilde \lambda_ i\) of \(A + \delta A\) is in \(I\) and that the associated eigenvector \(\widetilde x^ i\) has the same sign pattern as \(x^ i\).
Mathematics Subject Classification ID: 15A42
zbMATH DE Number: 519701
zbMATH Keywords: eigenvalue
zbMATH Keywords: eigenvector
zbMATH Keywords: perturbation
zbMATH Keywords: sign pattern
reviewed by: Hans Havlicek
MaRDI profile type: Publication
full work available at URL: 0024-3795(94)90315-8
OpenAlex ID: W2056588695
cites work: Norms and exclusion theorems
cites work: Q3201643
cites work: The Interval Eigenvalue Problem
cites work: On the range of eigenvalues of an interval matrix
description: scientific article; zbMATH DE number 519701