Numerical range circumscribed by two polygons

Hwa Long Gau, Pei Yuan Wu

Research output: Contribution to journalArticlepeer-review

18 Scopus citations

Abstract

We show that, for any 2n+2 distinct points a1,a 1′,a2,a2′,⋯,a n+1,an+1′ (in this order) on the unit circle, there is an n-by-n matrix A, unique up to unitary equivalence, which has norm one and satisfies the conditions that it has all its eigenvalues in the open unit disc, In-A*A has rank one and its numerical range is circumscribed by the two (n+1)-gons a1a2⋯an+1 and a′1a′2⋯a′n+1. This generalizes the classical result of the existence of a conical curve circumscribed by two triangles which are already inscribed on another conical curve.

Original languageEnglish
Pages (from-to)155-170
Number of pages16
JournalLinear Algebra and Its Applications
Volume382
Issue number1-3
DOIs
StatePublished - 1 May 2004

Keywords

  • Numerical range
  • Polygon
  • S -matrix

Fingerprint

Dive into the research topics of 'Numerical range circumscribed by two polygons'. Together they form a unique fingerprint.

Cite this