Bounds for ratios of eigenvalues using traces |
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| Authors: | Jorma Kaarlo Merikoski George PH Styan Henry Wolkowicz |
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| Affiliation: | Department of Mathematical Sciences University of Tampere P.O. Box 607 SF-33101 Tampere 10, Finland;Department of Mathematics and Statistics McGill University 805 ouest, rue Sherbrooke Montréal, Québec, Canada H3A 2K6;Department of Mathematics The University of Alberta Edmonton, Alberta, Canada T6G 2G1 |
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| Abstract: | Let A be an n × n matrix with real eigenvalues λ1 ? … ? λn, and let 1 ? k < l ? n. Bounds involving trA and trA2 are introduced for λk/λl, (λk ? λl)/(λk + λl), and {kλk + (n ? l + 1)λl}2/{kλ2k + (n ? l + 1)λ2l}. Also included are conditions for λl >; 0 and for λk + λl > 0. |
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