On flat portions on the boundary of the numerical range

Ethan S. Brown, Ilya M. Spitkovsky

Research output: Contribution to journalArticlepeer-review

Abstract

The paper is devoted to matrices with flat portions on the boundary of their numerical range. A constructive criterion for such portions to exist is obtained in case of tridiagonal matrices, and a particular case of continuant matrices is considered. As an application, the cases of (arbitrary) 3×3 and 4×4 matrices are treated. It is shown, in particular, that the sharp bound for the number of flat portions on the boundary of the numerical range for 4×4 matrices is four (three, if the matrices are assumed unitarily irreducible).

Original languageEnglish (US)
Pages (from-to)75-109
Number of pages35
JournalLinear Algebra and Its Applications
Volume390
Issue number1-3
DOIs
StatePublished - Oct 1 2004

Keywords

  • Numerical range
  • Tridiagonal matrices
  • Unitary (ir)reducibility

ASJC Scopus subject areas

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

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