Domains containing the field of values of a matrix |
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| Authors: | AI Mees DP Atherton |
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| Institution: | Department of Pure Mathematics and Mathematical Statistics Cambridge University Mill Lane Cambridge, CB2 1SB, England;Department of Electrical Engineering University of New Brunswick Fredericton, New Brunswick, Canada E3B 5A3 |
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| Abstract: | Two groups of estimates are given for the field of values of a general complex matrix. The first group gives a domain containing both the field of values and the convex hull of the diagonal elements, while the second group gives a domain containing both the field of values and the convex hull of the eigenvalues. The domain given by the second group reduces to the smallest domain possible if the matrix is normal. The results have useful applications in control theory and in stability theory for differential equations. |
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