The possible shapes of numerical ranges

J. William Helton, Ilya Spitkovsky

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)607-611
Number of pages5
JournalOperators and Matrices
Volume6
Issue number3
DOIs
StatePublished - Sep 1 2012

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Numerical Range
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Keywords

  • Linear matrix inequalities
  • Numerical range

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory

Cite this

The possible shapes of numerical ranges. / William Helton, J.; Spitkovsky, Ilya.

In: Operators and Matrices, Vol. 6, No. 3, 01.09.2012, p. 607-611.

Research output: Contribution to journalArticle

William Helton, J. ; Spitkovsky, Ilya. / The possible shapes of numerical ranges. In: Operators and Matrices. 2012 ; Vol. 6, No. 3. pp. 607-611.
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