Eigenvalues of graded matrices and the condition numbers of a multiple eigenvalue
type: Item
instance of: scholarly article
title: Eigenvalues of graded matrices and the condition numbers of a multiple eigenvalue
zbMATH Open document ID: 0697.65027
DOI: 10.1007/BF01385650
author: N. E. Zubov
published in: Numerische Mathematik
publication date: 1991-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/133526
review text: This paper concerns two closely related topics: the behavior of the eigenvalues of graded matrices and the perturbation of a nondefective multiple eigenvalue. We will show that the eigenvalues of a graded matrix tend to share the graded structure of the matrix and give precise conditions insuring that this tendency is realized. These results are then applied to show that the secants of the canonical angles between the left and right invariant subspaces of a multiple eigenvalue tend to characterize its behaviour when its matrix is slightly perturbed.
reviewed by: Genkai Zhang
Mathematics Subject Classification ID: 65F15
Mathematics Subject Classification ID: 65F35
zbMATH DE Number: 4143341
zbMATH Keywords: condition number
zbMATH Keywords: graded matrices
zbMATH Keywords: perturbation
zbMATH Keywords: multiple eigenvalue
zbMATH Keywords: invariant subspaces
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4143341