Operators and Matrices
Which convex subsets of C are the numerical range W(A) of some matrix A? This paper gives a precise characterization of these sets. In addition to this we show that for any A there exists a symmetric B of the same size such that W(A) = W(B) thereby settling an open question from .
Helton, J. W., & Spitkovsky, I. M. (2011). The possible shapes of numerical ranges. arXiv preprint arXiv:1104.4587.