The q-numerical range of a nilpotent 4 x 4 matrix
نویسندگان
چکیده
منابع مشابه
When is the numerical range of a nilpotent matrix circular?
The problem formulated in the title is investigated. The case of nilpotent matrices of size at most 4 allows a unitary treatment. The numerical range of a nilpotent matrix M of size at most 4 is circular if and only if the traces trM M and trM M are null. The situation becomes more complicated as soon as the size is 5. The conditions under which a 5 5 nilpotent matrix has circular numerical ran...
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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: International Mathematical Forum
سال: 2014
ISSN: 1314-7536
DOI: 10.12988/imf.2014.49157