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: [email protected] (H.-L. Gau), [email protected] (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 -