More bounds for elgenvalues using traces |
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Authors: | Henry Wolkowicz George PH Styan |
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Institution: | Department of Mathematics Dalhousie University Halifax, Nova Scotia, Canada B3H 4H8;Department of Mathematics McGill University 805 Sherbrooke Street West Montréal, Quebec, Canada H3A 2K6 |
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Abstract: | Let the n × n complex matrix A have complex eigenvalues λ1,λ2,…λn. Upper and lower bounds for Σ(Reλi)2 are obtained, extending similar bounds for Σ|λi|2 obtained by Eberlein (1965), Henrici (1962), and Kress, de Vries, and Wegmann (1974). These bounds involve the traces of A1A, B2, C2, and D2, where , , and , and strengthen some of the results in our earlier paper “Bounds for eigenvalues using traces” in Linear Algebra and Appl. 12]. |
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