Search

MiS Preprint Repository

Delve into the future of research at MiS with our preprint repository. Our scientists are making groundbreaking discoveries and sharing their latest findings before they are published. Explore repository to stay up-to-date on the newest developments and breakthroughs.

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