Numerical range circumscribed by two polygons
نویسندگان
چکیده
We show that, for any 2n+ 2 distinct points a1, a′ 1, a2, a′ 2, . . . , an+1, a′ n+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. © 2004 Elsevier Inc. All rights reserved. AMS classification: 15A60; 51A05
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