Helton, J. William; Spitkovsky, I. M. The possible shapes of numerical ranges. (English) Zbl 1270.15014 Oper. Matrices 6, No. 3, 607-611 (2012). 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. Reviewer: João R. Cardoso (Coimbra) Cited in 2 ReviewsCited in 15 Documents 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 Keywords:numerical range; linear matrix inequalities; symmetric matrix PDF BibTeX XML Cite \textit{J. W. Helton} and \textit{I. M. Spitkovsky}, Oper. Matrices 6, No. 3, 607--611 (2012; Zbl 1270.15014) Full Text: DOI Link