Weyl-type relative perturbation bounds for eigensystems of Hermitian matrices
type: Item
instance of: scholarly article
title: Weyl-type relative perturbation bounds for eigensystems of Hermitian matrices
zbMATH Open document ID: 0957.15014
DOI: 10.1016/S0024-3795(00)00018-5
author: Froilán M. Dopico
author: Julio Moro
author: Juan M. Molera
published in: Linear Algebra and its Applications
publication date: 2001-03-20T00:00:00Z
review text: A Weyl type relative perturbation bound for the eigenvalues of \(A+E\) and \(A\), both positive definite, is extended to the indefinite Hermitian matrix case. This is applied to give a natural order perturbation bound for arbitrary Hermitian matrices \(A\) whose normal square root \(A^{1/2}\) satisfies \(\|A^{-1/2}EA^{-1/2}\|_2 \leq 1\) for the perturbation \(E\) that affects \(A\). Likewise there are applications to the variation of perturbed eigenspaces, perturbed singular values and singular vectors.
reviewed by: Frank Uhlig
Mathematics Subject Classification ID: 15A42
Mathematics Subject Classification ID: 15B57
zbMATH DE Number: 1443440
zbMATH Keywords: eigenvalue perturbation
zbMATH Keywords: eigenvector perturbation
zbMATH Keywords: perturbation bound
zbMATH Keywords: Hermitean matrices
zbMATH Keywords: singular values
zbMATH Keywords: singular vectors
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1443440