TY - JOUR

T1 - Numerical range circumscribed by two polygons

AU - Gau, Hwa Long

AU - Wu, Pei Yuan

N1 - Funding Information:
Research supported by the National Science Council of the Republic of China. ∗ Corresponding author. E-mail addresses: hlgau@math.ncu.edu.tw (H.-L. Gau), pywu@math.nctu.edu.tw (P.Y. Wu).

PY - 2004/5/1

Y1 - 2004/5/1

N2 - 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.

AB - 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.

KW - Numerical range

KW - Polygon

KW - S -matrix

UR - http://www.scopus.com/inward/record.url?scp=1842609586&partnerID=8YFLogxK

U2 - 10.1016/j.laa.2003.12.003

DO - 10.1016/j.laa.2003.12.003

M3 - 期刊論文

AN - SCOPUS:1842609586

SN - 0024-3795

VL - 382

SP - 155

EP - 170

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

IS - 1-3

ER -