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Numerical ranges of companion matrices

โœ Scribed by Hwa-Long Gau; Pei Yuan Wu

Publisher
Elsevier Science
Year
2007
Tongue
English
Weight
182 KB
Volume
421
Category
Article
ISSN
0024-3795

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โœฆ Synopsis

We show that an n-by-n companion matrix A can have at most n line segments on the boundary NW (A) of its numerical range W(A), and it has exactly n line segments on NW (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 โŠ• A 2 of two (n/2)-by-(n/2) companion matrices

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