The distance between the eigenvalues of Hermitian matrices
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- by Rajendra Bhatia PDF
- Proc. Amer. Math. Soc. 96 (1986), 41-42 Request permission
Abstract:
It is shown that the minmax principle of Ky Fan leads to a quick simple derivation of a recent inequality of V. S. Sunder giving a lower bound for the spectral distance between two Hermitian matrices. This brings out a striking parallel between this result and an earlier known upper bound for the spectral distance due to L. Mirsky.References
- Rajendra Bhatia, Analysis of spectral variation and some inequalities, Trans. Amer. Math. Soc. 272 (1982), no. 1, 323–331. MR 656492, DOI 10.1090/S0002-9947-1982-0656492-X
- Ky Fan, On a theorem of Weyl concerning eigenvalues of linear transformations. I, Proc. Nat. Acad. Sci. U.S.A. 35 (1949), 652–655. MR 34519, DOI 10.1073/pnas.35.11.652
- Albert W. Marshall and Ingram Olkin, Inequalities: theory of majorization and its applications, Mathematics in Science and Engineering, vol. 143, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1979. MR 552278
- L. Mirsky, Symmetric gauge functions and unitarily invariant norms, Quart. J. Math. Oxford Ser. (2) 11 (1960), 50–59. MR 114821, DOI 10.1093/qmath/11.1.50
- V. S. Sunder, On permutations, convex hulls, and normal operators, Linear Algebra Appl. 48 (1982), 403–411. MR 683234, DOI 10.1016/0024-3795(82)90123-9
Additional Information
- © Copyright 1986 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 96 (1986), 41-42
- MSC: Primary 15A42; Secondary 15A60
- DOI: https://doi.org/10.1090/S0002-9939-1986-0813806-4
- MathSciNet review: 813806