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The possible shapes of numerical ranges. (English) Zbl 1270.15014
This paper presents essentially two results related with numerical ranges. It gives a necessary and sufficient condition for a subset of the complex plane to be the numerical range of a certain matrix and it also shows that for a given matrix there always exists a symmetric matrix with the same numerical range.

MSC:
15A60 Norms of matrices, numerical range, applications of functional analysis to matrix theory
15A45 Miscellaneous inequalities involving matrices
15B57 Hermitian, skew-Hermitian, and related matrices
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