On eigenvalues and boundary curvature of the numerical range

Lauren Caston, Milena Savova, Ilya Spitkovsky, Nahum Zobin

Research output: Contribution to journalArticle

Abstract

Let A be an n×n matrix. By Donoghue's theorem, all corner points of its numerical range W(A) belong to the spectrum σ(A). It is therefore natural to expect that, more generally, the distance from a point p on the boundary ∂W(A) of W(A) to σ(A) should be in some sense bounded by the radius of curvature of ∂W(A) at p. We establish some quantitative results in this direction.

Original languageEnglish (US)
Pages (from-to)129-140
Number of pages12
JournalLinear Algebra and Its Applications
Volume322
Issue number1-3
DOIs
StatePublished - Jan 1 2001

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Numerical Range
Curvature
Eigenvalue
Radius of curvature
Theorem

Keywords

  • Curvature
  • Eigenvalues
  • Numerical range
  • Primary 47A12
  • Secondary 15A42, 14H50

ASJC Scopus subject areas

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

Cite this

On eigenvalues and boundary curvature of the numerical range. / Caston, Lauren; Savova, Milena; Spitkovsky, Ilya; Zobin, Nahum.

In: Linear Algebra and Its Applications, Vol. 322, No. 1-3, 01.01.2001, p. 129-140.

Research output: Contribution to journalArticle

Caston, Lauren ; Savova, Milena ; Spitkovsky, Ilya ; Zobin, Nahum. / On eigenvalues and boundary curvature of the numerical range. In: Linear Algebra and Its Applications. 2001 ; Vol. 322, No. 1-3. pp. 129-140.
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