Convexity of the Joint Numerical Range: Topological and Differential Geometric Viewpoints
نویسندگان
چکیده
The purpose of this paper is to show that the joint numerical range of am-tuple of n×n hermitian matrices is convex whenever the largest eigenvalue of an associated family of hermitian matrices parameterized by the (m − 1)-dimensional sphere has constant multiplicity and, as a more technical condition, the union over the sphere of the largest eigenvalue eigenspaces does not fill the full n-dimensional complex ∗Partially supported by the National Science Foundation grant ECS-98-02594.
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