The possible shapes of numerical ranges

J. William Helton; I. M. Spitkovsky

doi:10.7153/oam-06-41

The possible shapes of numerical ranges

J. William Helton, I. M. Spitkovsky

Mathematics

Research output: Contribution to journal › Article › peer-review

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].

Original language	English (US)
Pages (from-to)	607-611
Number of pages	5
Journal	Operators and Matrices
Volume	6
Issue number	3
DOIs	https://doi.org/10.7153/oam-06-41
State	Published - Sep 2012

Keywords

Linear matrix inequalities
Numerical range

ASJC Scopus subject areas

Analysis
Algebra and Number Theory

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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].",

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The possible shapes of numerical ranges

Abstract

Keywords

ASJC Scopus subject areas

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