Pre-images of extreme points of the numerical range, and applications

Ilya Spitkovsky, Stephan Weis

    Research output: Contribution to journalArticle

    Abstract

    We extend the pre-image representation of exposed points of the numerical range of a matrix to all extreme points. With that we characterize extreme points which are multiply generated, having at least two linearly independent pre-images, as the extreme points which are Hausdorff limits of flat boundary portions on numerical ranges of a sequence converging to the given matrix. These studies address the inverse numerical range map and the maximum-entropy inference map which are continuous functions on the numerical range except possibly at certain multiply generated extreme points. This work also allows us to describe closures of subsets of 3-by-3 matrices having the same shape of the numerical range.

    Original languageEnglish (US)
    Article numberoam-10-58
    Pages (from-to)1043-1058
    Number of pages16
    JournalOperators and Matrices
    Volume10
    Issue number4
    DOIs
    StatePublished - Dec 1 2016

    Fingerprint

    Numerical Range
    Extreme Points
    Multiplication
    Exposed Point
    Image Representation
    Maximum Entropy
    Continuous Function
    Closure
    Linearly
    Subset

    Keywords

    • Numerical range

    ASJC Scopus subject areas

    • Analysis
    • Algebra and Number Theory

    Cite this

    Pre-images of extreme points of the numerical range, and applications. / Spitkovsky, Ilya; Weis, Stephan.

    In: Operators and Matrices, Vol. 10, No. 4, oam-10-58, 01.12.2016, p. 1043-1058.

    Research output: Contribution to journalArticle

    Spitkovsky, Ilya ; Weis, Stephan. / Pre-images of extreme points of the numerical range, and applications. In: Operators and Matrices. 2016 ; Vol. 10, No. 4. pp. 1043-1058.
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