Numerical range circumscribed by two polygons

Hwa Long Gau, Pei Yuan Wu

研究成果: 雜誌貢獻期刊論文同行評審

18 引文 斯高帕斯(Scopus)

摘要

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.

原文???core.languages.en_GB???
頁(從 - 到)155-170
頁數16
期刊Linear Algebra and Its Applications
382
發行號1-3
DOIs
出版狀態已出版 - 1 5月 2004

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