An overview of relative \(\sin\Theta\) theorems for invariant subspaces of complex matrices
type: Item
instance of: scholarly article
title: An overview of relative \(\sin\Theta\) theorems for invariant subspaces of complex matrices
zbMATH Open document ID: 0964.65039
DOI: 10.1016/S0377-0427(00)00404-0
published in: Journal of Computational and Applied Mathematics
publication date: 2001-06-26T00:00:00Z
review text: A complex square matrix is assumed to possess an invariant subspace, and a change of this subspace under a perturbation is measured by a certain ``pricipal'' angle. For its sinus, a number of estimates is reviewed/listed for both the additive and multiplicative perturbations and different assumptions about the matrix. The review, a successor of similar surveys, offers another set of explanations why certain high-accuracy diagonalization methods are so reliable. It is well written and well understandable, with both the ideas and technicalities amply illustrated by the three-dimensional or partitioned examples.
reviewed by: Miloslav Znojil
Mathematics Subject Classification ID: 65F15
Mathematics Subject Classification ID: 15A42
Mathematics Subject Classification ID: 65F35
zbMATH DE Number: 1546544
zbMATH Keywords: invariant subspace
zbMATH Keywords: rotation by perturbation
zbMATH Keywords: bounds on angle
zbMATH Keywords: dependence on eigenvalues
zbMATH Keywords: grading and scaling
zbMATH Keywords: reliable computation of eigenvectors
zbMATH Keywords: numerical examples
author: Ilse C. F. Ipsen
MaRDI profile type: Publication
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full work available at URL: s0377-0427(00)00404-0
OpenAlex ID: W1996522765
description: scientific article; zbMATH DE number 1546544