Bounds for the determinant of the sum of hermitian matrices
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- by Miroslav Fiedler PDF
- Proc. Amer. Math. Soc. 30 (1971), 27-31 Request permission
Abstract:
Best possible lower and upper bounds for the determinant of the sum of two hermitian matrices in terms of the eigenvalues of both matrices are obtained.References
- Edwin F. Beckenbach and Richard Bellman, Inequalities, Ergebnisse der Mathematik und ihrer Grenzgebiete, (N.F.), Band 30, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1961. MR 0158038
- G. H. Hardy, J. E. Littlewood, and G. Pólya, Inequalities, Cambridge, at the University Press, 1952. 2d ed. MR 0046395
- V. B. Lidskiĭ, On the characteristic numbers of the sum and product of symmetric matrices, Doklady Akad. Nauk SSSR (N.S.) 75 (1950), 769–772 (Russian). MR 0039686
- Helmut Wielandt, An extremum property of sums of eigenvalues, Proc. Amer. Math. Soc. 6 (1955), 106–110. MR 67842, DOI 10.1090/S0002-9939-1955-0067842-9
Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 30 (1971), 27-31
- MSC: Primary 15.55
- DOI: https://doi.org/10.1090/S0002-9939-1971-0286814-1
- MathSciNet review: 0286814