Perturbation bounds for the joint spectrum of commuting matrices
type: Item
instance of: scholarly article
title: Perturbation bounds for the joint spectrum of commuting matrices
zbMATH Open document ID: 1067.15015
published in: Linear Algebra and its Applications
publication date: 2004-08-04T00:00:00Z
review text: Let \(A=(A_1,A_2,\dots,A_m)\) and \(B=(B_1,B_2,\dots,B_m)\) be commuting \(m\)-tuples of \(n\times n\) matrices. The main results establish upper bounds for the distance to the spectrum of \(B\) of an arbitrary \(m\)-tuple \(\lambda\) in the spectrum of \(A\), in terms of a generalized Schur decomposition of \(B\) and certain associated Clifford operators, distinguishing the cases when both \(A\) and \(B\) have real spectra or not.
reviewed by: Aurelian Gheondea
Mathematics Subject Classification ID: 15A42
Mathematics Subject Classification ID: 15A66
Mathematics Subject Classification ID: 15A27
zbMATH DE Number: 2081235
zbMATH Keywords: joint spectrum
zbMATH Keywords: joint eigenvalues
zbMATH Keywords: perturbation bounds
zbMATH Keywords: Clifford algebra
zbMATH Keywords: commuting matrices
author: Daniel Z. Freedman
MaRDI profile type: Publication
full work available at URL: j.laa.2003.12.012
OpenAlex ID: W2057126347
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DOI: 10.1016/J.LAA.2003.12.012
description: scientific article; zbMATH DE number 2081235