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Numerical ranges of reducible companion matrices

โœ Scribed by Hwa-Long Gau

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
196 KB
Volume
432
Category
Article
ISSN
0024-3795

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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-

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A Banach algebraic approach is proposed to study the asymptotic bchaviour of the numerical ranges of certain (finite) approximation matrices of {infinite) operators. The approach works for large classes of approximation methods; it is examined in detail here for the finite sections of Toeplitz opera

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