標題: Numerical range circumscribed by two polygons
作者: Gau, HL
Wu, PY
應用數學系
Department of Applied Mathematics
關鍵字: numerical range;Ln-matrix;polygon
公開日期: 1-May-2004
摘要: We show that, for any 2n+2 distinct points a(1), a'(1), a(2), a'(2),...,a(n+1), a'(n+1) (in this order) on the unit circle, there is an n-by-n matrix A. unique LIP to Unitary equivalence, which has norm one and satisfies the conditions that it has all its eigenvalues in the open unit disc, I-n-A*A has rank one and its numerical range is circumscribed by the two (n+1)-gons a(1)a(2)...a(n+1) and a'(1)a'(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. (C) 2004 Elsevier Inc. All rights reserved.
URI: http://dx.doi.org/10.1016/j.laa.2003.12.003
http://hdl.handle.net/11536/26807
ISSN: 0024-3795
DOI: 10.1016/j.laa.2003.12.003
期刊: LINEAR ALGEBRA AND ITS APPLICATIONS
Volume: 382
Issue: 
起始頁: 155
結束頁: 170
Appears in Collections:Articles


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