The Possible Shapes of Numerical Ranges

Authors

J. William Helton
I. M. Spitkovsky, William & MaryFollow

Document Type

Article

Department/Program

Mathematics

Journal Title

Operators and Matrices

Pub Date

2012

Volume

6

Issue

3

First Page

607

Abstract

Which convex subsets of C 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 B of the same size such that W(A) = W(B) thereby settling an open question from [2].

Recommended Citation

Helton, J. William and Spitkovsky, I. M., The Possible Shapes of Numerical Ranges (2012). Operators and Matrices, 6(3), 607-611.
10.7153/oam-06-41

DOI

10.7153/oam-06-41