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

    William Helton, J., & Spitkovsky, I. (2012). The possible shapes of numerical ranges. Operators and Matrices, 6(3), 607-611. https://doi.org/10.7153/oam-06-41

    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, I 2012, 'The possible shapes of numerical ranges', Operators and Matrices, vol. 6, no. 3, pp. 607-611. https://doi.org/10.7153/oam-06-41
    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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