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MiS Preprint

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

Eugene Gutkin, Edmond Jonckheere and Michael Karow


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.

joint numerical range, support function, highest eigenvalue

Related publications

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