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arXiv · 1104.4587

The possible shapes of numerical ranges

J. William Helton·Ilya M. Spitkovsky
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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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J. William Helton, Ilya M. Spitkovsky. 2011-04-23. The possible shapes of numerical ranges. https://arxiv.org/abs/1104.4587

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