TheC-numerical range of matrices is star-shaped

1 November 1996

journal article
research article
Published by Taylor & Francis in Linear and Multilinear Algebra

Vol. 41 (3) , 245-250
https://doi.org/10.1080/03081089608818479

Abstract

Let A C be n× ncomplex matrices. We prove in the affirmative the conjecture that the C-numerical range of A, defined by is always star-shaped with respect to star-center (tr A)(tr C)/ n. This result is equivalent to that the image of the unitary orbit {U ^∗ AU:U} of A under any complex linear functional is always star-shaped.

Keywords

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