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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
1/2003

Convexity of the Joint Numerical Range: Topological and Differential Geometric Viewpoints

Eugene Gutkin, Edmond Jonckheere and Michael Karow

Abstract

We show that the outer boundary of the joint numerical range of any number, $m$, of hermitian matrices is convex if the multiplicity of the largest eigenvalue of the associated hermitian matrix is constant. Thus for $m>3$ the problem of convexity of the joint numerical range is essentially topological.

Furthermore, our sufficient condition for convexity of the joint numerical range is also necessary for its stable convexity.

Received:
Jan 2, 2003
Published:
Jan 2, 2003
Keywords:
joint numerical range, support function, highest eigenvalue

Related publications

inJournal
2004 Repository Open Access
Eugene Gutkin, EA Jonckheere and M Karow

Convexity of the joint numerical range: topological and differential geometric viewpoints

In: Linear algebra and its applications, 376 (2004), pp. 143-171