The numerical range of 3 X 3 matrices

Dennis S. Keeler, Leiba Rodman, Ilya Spitkovsky

    Research output: Contribution to journalArticle

    Abstract

    Let A be an n X n complex matrix. Then the numerical range of A, W(A), is defined to be {x*Ax : x ∈ ℂn, x*x = 1}. In this article a series of tests is given, allowing one to determine the shape of W( A) for 3 X 3 matrices. Reconstruction of A, up to unitary similarity, from W(A) is also examined.

    Original languageEnglish (US)
    Pages (from-to)115-139
    Number of pages25
    JournalLinear Algebra and Its Applications
    Volume252
    Issue number1-3
    DOIs
    StatePublished - Jan 1 1997

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    ASJC Scopus subject areas

    • Algebra and Number Theory
    • Numerical Analysis
    • Geometry and Topology
    • Discrete Mathematics and Combinatorics

    Cite this

    The numerical range of 3 X 3 matrices. / Keeler, Dennis S.; Rodman, Leiba; Spitkovsky, Ilya.

    In: Linear Algebra and Its Applications, Vol. 252, No. 1-3, 01.01.1997, p. 115-139.

    Research output: Contribution to journalArticle

    Keeler, DS, Rodman, L & Spitkovsky, I 1997, 'The numerical range of 3 X 3 matrices', Linear Algebra and Its Applications, vol. 252, no. 1-3, pp. 115-139. https://doi.org/10.1016/0024-3795(95)00674-5
    Keeler, Dennis S. ; Rodman, Leiba ; Spitkovsky, Ilya. / The numerical range of 3 X 3 matrices. In: Linear Algebra and Its Applications. 1997 ; Vol. 252, No. 1-3. pp. 115-139.
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