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Convexity of the joint numerical range: Topological and differential geometric viewpoints. (English) Zbl 1050.15026
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.

MSC:
15A60 Norms of matrices, numerical range, applications of functional analysis to matrix theory
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