On worst-case condition numbers of a nondefective multiple eigenvalue
type: Item
instance of: scholarly article
title: On worst-case condition numbers of a nondefective multiple eigenvalue
zbMATH Open document ID: 0821.65021
author: Ji-guang Sun
published in: Numerische Mathematik
publication date: 1995-04-02T00:00:00Z
full work available at URL: https://eudml.org/doc/133621
review text: This paper shows that the quantities \(c_ j (A; \lambda_ 1) \equiv (\prod^ j_{k=1} c_ k (A; \lambda_ 1))^{1/j}\), \(j = 1, \dots, r\), are the worst-case condition numbers of the multiple eigenvalue \(\lambda_ 1\), where \(\lambda_ 1\) is a nondefective multiple eigenvalue of multiplicity \(r\) of an \(n \times n\) complex matrix \(A\), and \(c_ 1 (A; \lambda_ 1) \geq \cdots \geq c_ r (A; \lambda_ 1)\) are the secants of the canonical angles between the left and right invariant subspaces of \(A\) corresponding to the multiple eigenvalue \(\lambda_ 1\). A simple example to test its conclusions is illustrated in the last section.
Mathematics Subject Classification ID: 65F15
Mathematics Subject Classification ID: 65F35
zbMATH DE Number: 739417
zbMATH Keywords: perturbation
zbMATH Keywords: numerical example
zbMATH Keywords: worst-case condition numbers
zbMATH Keywords: multiple eigenvalue
zbMATH Keywords: invariant subspaces
reviewed by: Shenquan Xie
MaRDI profile type: Publication
OpenAlex ID: W2092974719
DOI: 10.1007/S002110050098
description: scientific article; zbMATH DE number 739417