On the shape of numerical range of matrix polynomials
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Psarrakos, P
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Nakazato, H
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The numerical range of an n x n matrix polynomial P (lambda) = A(m)lambda (m) +...+ A(1)lambda + A(0) is defined by W(P) = {lambda is an element of C: x*P(lambda )x = 0, x is an element of C-n, x not equal 0}. In this paper, we investigate the shape of W(P) by using the notion of local dimension. The numerical range of first order matrix polynomials is always simply connected. The special cases of diagonal matrix polynomials and 2 x 2 matrix polynomials are also considered. (C) 2001 Elsevier Science Inc. All rights reserved.
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