A normal form is derived for finite sets of doubly commuting matrices, under simultaneous unitary similarity. The matrices need not be normal, but they commute with each other and with the adjoints of each other. The normal form is further used to study joint numerical ranges of doubly commuting mat
The numerical range of products of normal matrices
โ Scribed by S.W. Drury
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 646 KB
- Volume
- 288
- Category
- Article
- ISSN
- 0024-3795
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โฆ Synopsis
In an earlier paper, the author developed a formula Ibr the trace class multiplier norm of a matrix of rank at most 2. In this article, applications of this formula are given. In the main result we suppose that .I"1 ..... .L and g~,... ,g,, are given sets of complex numbers. A description is given of the union of the numerical ranges of the product FG as F and G run over all n ร n normal matrices with the given sets as eigenvalues.
๐ SIMILAR VOLUMES
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 โ A 2 of two (n/2)-by-
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