TheC-numerical range of matrices is star-shaped
Wai-Shun Cheung, Nam‐Kiu Tsing · Linear and Multilinear Algebra · 1996
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.