Effect of linear perturbation on spectra of matrices
type: Item
instance of: scholarly article
title: Effect of linear perturbation on spectra of matrices
zbMATH Open document ID: 1030.15018
DOI: 10.1016/S0024-3795(02)00692-4
published in: Linear Algebra and its Applications
publication date: 2003-07-30T00:00:00Z
review text: The sensitivity of the eigenvalues of a matrix \(A\) under a linear perturbation \(A(t) = A + tE\) is studied. The aim of such studies is to learn about the split-up of repeated eigenvalues of \(A\) in \(A(t)\). It is known that there are essentially three kinds of behaviour here: In general there are finitely stable, infinitely stable, and unstable eigenvalues. This paper primarily studies perturbation effects on the unstable eigenvalues and looks at the distribution of the perturbed spectra. Isospectral perturbations \(E\) of \(A\) in \(A(t)\) for some or all values of \(t\) are also characterized here.
Mathematics Subject Classification ID: 15A42
Mathematics Subject Classification ID: 65F15
zbMATH DE Number: 1956809
zbMATH Keywords: eigenvalue sensitivity
zbMATH Keywords: perturbation
zbMATH Keywords: spectral variety
zbMATH Keywords: isospectral perturbation
author: Rafikul Alam
author: Shreemayee Bora
reviewed by: Frank Uhlig
MaRDI profile type: Publication
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full work available at URL: s0024-3795(02)00692-4
OpenAlex ID: W2084448528
description: scientific article; zbMATH DE number 1956809