Numerical range of matrices and Levinger's theorem
نویسندگان
چکیده
منابع مشابه
Numerical Range for Random Matrices
We analyze the numerical range of high-dimensional random matrices, obtaining limit results and corresponding quantitative estimates in the non-limit case. For a large class of random matrices their numerical range is shown to converge to a disc. In particular, numerical range of complex Ginibre matrix almost surely converges to the disk of radius √ 2. Since the spectrum of non-hermitian random...
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The q-numerical range (0 ≤ q ≤ 1) of an n × n matrix polynomial P (λ) = Amλ m + · · ·+ A1λ + A0 is defined by Wq(P ) = {λ ∈ C : y∗P (λ)x = 0, x, y ∈ C, x∗x = y∗y = 1, y∗x = q}. In this paper, we investigate the boundary and the shape of Wq(P ), using the notion of local dimension. We also obtain that the q-numerical range of first order matrix polynomials is always simply connected. Moreover, t...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1995
ISSN: 0024-3795
DOI: 10.1016/0024-3795(94)00073-m