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

Ilya M. Spitkovsky, Stephan Weis

Research output: Contribution to journalArticlepeer-review


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
Issue number4
StatePublished - Dec 2016


  • Numerical range

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory


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