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Numerical range for random matrices

✍ Scribed by Collins, Benoît; Gawron, Piotr; Litvak, Alexander E.; Życzkowski, Karol

Book ID
121704356
Publisher
Elsevier Science
Year
2014
Tongue
English
Weight
572 KB
Volume
418
Category
Article
ISSN
0022-247X

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✍ Hwa-Long Gau; Pei Yuan Wu 📂 Article 📅 2007 🏛 Elsevier Science 🌐 English ⚖ 182 KB

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 ⊕ 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