3 × 3 matrices with a flat portion on the boundary of the numerical range

L. Rodman, Ilya Spitkovsky

Research output: Contribution to journalArticle

Abstract

The set of unitarily irreducible complex 3 × 3 matrices whose numerical range has a flat portion is explicitly described. It is proved that the set is connected, and real analytic properties of the set are studied. Connectedness of the sets of unitarily irreducible 3 × 3 matrices having two other possible shapes of their numerical ranges is proved as well.

Original languageEnglish (US)
Pages (from-to)193-207
Number of pages15
JournalLinear Algebra and Its Applications
Volume397
Issue number1-3
DOIs
StatePublished - Mar 1 2005

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Numerical Range
Connectedness

Keywords

  • 3 × 3 matrices
  • Flat portion
  • Numerical range

ASJC Scopus subject areas

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

Cite this

3 × 3 matrices with a flat portion on the boundary of the numerical range. / Rodman, L.; Spitkovsky, Ilya.

In: Linear Algebra and Its Applications, Vol. 397, No. 1-3, 01.03.2005, p. 193-207.

Research output: Contribution to journalArticle

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