Numerical ranges of reducible companion matrices

Please use this identifier to cite or link to this item: http://ir.lib.ncu.edu.tw/handle/987654321/51137

Title:	Numerical ranges of reducible companion matrices
Authors:	Gau,HL
Contributors:	數學系
Date:	2010
Issue Date:	2012-03-27 18:22:58 (UTC+8)
Publisher:	國立中央大學
Abstract:	In this paper, we show that a reducible companion matrix is completely determined by its numerical range, that is, if two reducible companion matrices have the same numerical range, then they must equal to each other. We also obtain a criterion for a reducible companion matrix to have an elliptic numerical range, put more precisely, we show that the numerical range of an n-by-n reducible companion matrix C is an elliptic disc if and only if C is unitarily equivalent to A circle plus B, where A epsilon M(n-2), B epsilon M(2) with sigma(B) = {a omega(1),a omega(2)}, omega(n)(1) = omega(n)(2) = 1, omega(1) not equal omega(2), and vertical bar a vertical bar >= (vertical bar omega(1) + omega(2)vertical bar + root vertical bar omega(1) + omega(2)vertical bar(2) + 4(1 + 2 cos(pi/n)))/2. (C) 2009 Elsevier Inc. All rights reserved.
Relation:	LINEAR ALGEBRA AND ITS APPLICATIONS
Appears in Collections:	[Department of Mathematics] journal & Dissertation

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