The product field of values

Daniel Corey, Charles R. Johnson, Ryan Kirk, Brian Lins, Ilya Spitkovsky

    Research output: Contribution to journalArticle

    Abstract

    For two n-by-n matrices, A,B, the product field of values is the set P(A,B)={〈Ax,x〉〈Bx,x〉:x∈Cn,||x||=1}. In this paper, we establish basic properties of the product field of values. The main results are a proof that the product field is a simply connected subset of the complex plane and a characterization of matrix pairs for which the product field has nonempty interior.

    Original languageEnglish (US)
    Pages (from-to)2155-2173
    Number of pages19
    JournalLinear Algebra and Its Applications
    Volume438
    Issue number5
    DOIs
    StatePublished - Mar 1 2013

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    Field of Values
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    Keywords

    • Field of values
    • Numerical range

    ASJC Scopus subject areas

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

    Cite this

    Corey, D., Johnson, C. R., Kirk, R., Lins, B., & Spitkovsky, I. (2013). The product field of values. Linear Algebra and Its Applications, 438(5), 2155-2173. https://doi.org/10.1016/j.laa.2012.09.028

    The product field of values. / Corey, Daniel; Johnson, Charles R.; Kirk, Ryan; Lins, Brian; Spitkovsky, Ilya.

    In: Linear Algebra and Its Applications, Vol. 438, No. 5, 01.03.2013, p. 2155-2173.

    Research output: Contribution to journalArticle

    Corey, D, Johnson, CR, Kirk, R, Lins, B & Spitkovsky, I 2013, 'The product field of values', Linear Algebra and Its Applications, vol. 438, no. 5, pp. 2155-2173. https://doi.org/10.1016/j.laa.2012.09.028
    Corey D, Johnson CR, Kirk R, Lins B, Spitkovsky I. The product field of values. Linear Algebra and Its Applications. 2013 Mar 1;438(5):2155-2173. https://doi.org/10.1016/j.laa.2012.09.028
    Corey, Daniel ; Johnson, Charles R. ; Kirk, Ryan ; Lins, Brian ; Spitkovsky, Ilya. / The product field of values. In: Linear Algebra and Its Applications. 2013 ; Vol. 438, No. 5. pp. 2155-2173.
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