The possible shapes of numerical ranges. (English) Zbl 1270.15014

Helton, J. William; Spitkovsky, I. M.

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)

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