The possible shapes of numerical ranges

J. William Helton, I. M. Spitkovsky

Research output: Contribution to journalArticlepeer-review


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
Issue number3
StatePublished - Sep 2012


  • Linear matrix inequalities
  • Numerical range

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory


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