Absolute and relative perturbation bounds for invariant subspaces of matrices
type: Item
instance of: scholarly article
title: Absolute and relative perturbation bounds for invariant subspaces of matrices
zbMATH Open document ID: 0949.15025
DOI: 10.1016/S0024-3795(99)00104-4
author: Ilse C. F. Ipsen
published in: Linear Algebra and its Applications
publication date: 2000-12-05T00:00:00Z
review text: This paper considers complex nonsingular \(n\times n\) matrices \(A\) and perturbed matrices \(A+E\) and derives absolute and relative bounds on the angle between a true and a perturbed invariant subspace, expressed in the Euclidean and the Frobenius norms, and containing \(\|E\|\) and an absolute separation, and \(\|A^{-1}E\|\) and a relative separation, respectively. With respect to relative bounds, no restrictions are placed on \(A\), on \(E\), or on the dimension of the subspaces. The bounds can be expressed in terms of subspace bases. For diagonalizable matrices the separations are expressed in terms of eigenvalues.
reviewed by: Erwin O. Kreyszig
Mathematics Subject Classification ID: 15A42
Mathematics Subject Classification ID: 65F15
zbMATH DE Number: 1443442
zbMATH Keywords: perturbation bounds
zbMATH Keywords: subspace bases
zbMATH Keywords: invariant subspace
zbMATH Keywords: eigenvalues
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1443442