Numerical range circumscribed by two polygons

Hwa Long Gau, Pei Yuan Wu

Research output: Contribution to journalArticlepeer-review

19 Scopus citations


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
Issue number1-3
StatePublished - 1 May 2004


  • Numerical range
  • Polygon
  • S -matrix


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