The possible shapes of numerical ranges
J. William Helton, Ilya M. Spitkovsky · Operators and Matrices · 2012
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