A formula for the 2-norm distance from a matrix to the set of matrices with multiple eigenvalues
type: Item
instance of: scholarly article
title: A formula for the 2-norm distance from a matrix to the set of matrices with multiple eigenvalues
zbMATH Open document ID: 0972.15011
author: A. Malyshev
published in: Numerische Mathematik
publication date: 2001-11-18T00:00:00Z
review text: The author proves that the 2-norm distance from an \(n\times n\) matrix \(A\) to the matrices that have a multiple eigenvalue \(\lambda\) can be computed as the maximum with respect to \(\gamma\) of the second-lowest singular value of the \(2n\times 2n\) matrices with block-diagonal \(A-\lambda I\) in both entries and off-diagonal elements \(0\) and \(\gamma I\). Therefore, he can identify the 2-norm distance from \(A\) to the set of matrices with multiple eigenvalues -- and he is also able to give a constructive description of a minimizing matrix.
reviewed by: Tage Bai Andersen
Mathematics Subject Classification ID: 15A42
zbMATH DE Number: 1355442
zbMATH Keywords: 2-norm distance
zbMATH Keywords: singular value
zbMATH Keywords: multiple eigenvalues
MaRDI profile type: Publication
full work available at URL: s002110050458
OpenAlex ID: W2001760418
DOI: 10.1007/S002110050458
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description: scientific article; zbMATH DE number 1355442