Convexity of the joint numerical range: Topological and differential geometric viewpoints.
type: Item
instance of: scholarly article
title: Convexity of the joint numerical range: Topological and differential geometric viewpoints.
zbMATH Open document ID: 1050.15026
author: Michael Karow
author: Eugene Gutkin
author: Edmond Jonckheere
published in: Linear Algebra and its Applications
publication date: 2003-12-03T00:00:00Z
review text: The authors study the convexity of the joint numerical range of finite families of Hermitian matrices. A sufficient condition is expressed in terms of the behaviour of the largest eigenvalue of the linear combinations, over the real unit sphere of corresponding dimension, of the given matrices. Without this sufficient condition, the convexity of the joint numerical range (if it happens) may be destroyed by an arbitrarily small perturbation. The methods come from differential geometry and differential and algebraic topology.
Mathematics Subject Classification ID: 15A60
zbMATH DE Number: 2012704
zbMATH Keywords: Generalized numerical range
zbMATH Keywords: Convexity
zbMATH Keywords: Eigenvalue crossing
zbMATH Keywords: Matrix pencil
zbMATH Keywords: Singularity
zbMATH Keywords: Genericity
zbMATH Keywords: Fibration
zbMATH Keywords: Hermitian matrices
reviewed by: Jaroslav Zemánek
MaRDI profile type: Publication
Wikidata QID: Q115344967
full work available at URL: j.laa.2003.06.011
OpenAlex ID: W2002497815
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DOI: 10.1016/J.LAA.2003.06.011
description: scientific article; zbMATH DE number 2012704