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

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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

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