Title: | Numerical ranges of companion matrices |
Authors: | Gau, Hwa-Long Wu, Pei Yuan 應用數學系 Department of Applied Mathematics |
Keywords: | numerical range;companion matrix |
Issue Date: | 1-Mar-2007 |
Abstract: | We show that an n-by-n companion matrix A can have at most n line segments on the boundary a(A) of its numerical range W(A), and it has exactly n line segments on W(A) if and only if, for n odd, A is unitary, and, for n even, A is unitarily equivalent to the direct sum A(1) circle plus A(2) of two (n/2)-by-(n/2) companion matrices [GRAPHICS] with 1 <= vertical bar u vertical bar < tan(pi/n) + sec(pi/n). (c) 2006 Elsevier Inc. All rights reserved. |
URI: | http://dx.doi.org/10.1016/j.laa.2006.03.037 http://hdl.handle.net/11536/5101 |
ISSN: | 0024-3795 |
DOI: | 10.1016/j.laa.2006.03.037 |
Journal: | LINEAR ALGEBRA AND ITS APPLICATIONS |
Volume: | 421 |
Issue: | 2-3 |
Begin Page: | 202 |
End Page: | 218 |
Appears in Collections: | Conferences Paper |
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