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A generalization of rearrangement and matrix product inequalities. (English) Zbl 0966.90046

In the paper under review the authors discuss the inequalities for sequence rearrangements and matrix products, which have been considered recently in the papers: [N. Komaroff, Linear Algebra Appl. 140, 155-161 (1990; Zbl 0713.15006); Z. P. Yang, Northeast Math. J. 12, No. 1, 51-54 (1996; Zbl 0865.15016); B. E. Cain, R. A. Horn, and L. L. Li, Inequalities for monotonic arrangements of eigenvalues, Linear Algebra Appl. 222, 1-8 (1995; Zbl 0834.15009)].
First they analyze the results and point out some errors on inequalities in the first of these papers. Then they extend and improve their results and establish some inequalities, which as authors believe are the better generalization of the inequalities of Hardy, Littlewood, and Polya on monotonic rearrangements.

MSC:

90C05 Linear programming
15A45 Miscellaneous inequalities involving matrices
15A09 Theory of matrix inversion and generalized inverses
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References:

[1] Komaroff, N., Rearrangement and matrix product inequalites, Linear Algebra Appl., 1990, 140:155–161. · Zbl 0713.15006 · doi:10.1016/0024-3795(90)90227-4
[2] Yang, Z. P., A note on ”rearrangement and matrix product inequalities”, Northeast Math. J., 1996, 12(1):51–54. · Zbl 0865.15016
[3] Cain, B. E., Horn, R. A., Li, L. L., Inequalities for monotonic arrangements of eigenvalues, Linear Algebra Appl., 1995, 222:1–8. · Zbl 0834.15009 · doi:10.1016/0024-3795(93)00261-W
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