Stability of eigenvalues and spectral decompositions under linear perturbation
type: Item
instance of: scholarly article
title: Stability of eigenvalues and spectral decompositions under linear perturbation
zbMATH Open document ID: 1021.15012
DOI: 10.1016/S0024-3795(02)00549-9
published in: Linear Algebra and its Applications
publication date: 2003-05-04T00:00:00Z
review text: Given a square matrix \(A\), a fixed perturbation matrix \(E\), and \(A+tE\) the linear perturbations depending on the complex parameter \(t\), the main results of the paper pertain to: a) classification of the eigenvalues of \(A\) with respect to \(E\) into infinitely stable, finitely stable and unstable eigenvalues, and correspondingly providing various characterizations; b) analysis of the effect of the linear perturbations \(A+tE\) on spectral decompositions of \(A\) by introducing the dissociation and geometric separation of eigenvalues of \(A\) with respect to \(E\) and by characterization of the sensitivity of spectral decompositions of \(A\); c) geometric framework for the family \(A+tE\) in order to analyze various sensitivity issues associated with eigenvalues and spectral decompositions of \(A\) graphically.
reviewed by: Mihail Voicu
Mathematics Subject Classification ID: 15A42
zbMATH DE Number: 1903585
zbMATH Keywords: stable and unstable eigenvalues
zbMATH Keywords: spectrum decomposition
zbMATH Keywords: geometric separation of eigenvalues
zbMATH Keywords: perturbation matrix
author: Rafikul Alam
author: Shreemayee Bora
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1903585