The possible shapes of numerical ranges

Published 23 Apr 2011 in math.FA and math.AG | (1104.4587v1)

Abstract: Which convex subsets of the complex plane 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 matrix B of the same size such that W(A)=W(B).

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