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| Title: | Some inequalities for powers of positive definite matrices |
| Other Titles: | Inequalities for contraction matrices |
| Authors: | Abu-Asa'd, Ata Omar, Hirzallah |
| Keywords: | Matrix Analysis |
| Issue Date: | Jan-2017 |
| Publisher: | Mathematical Inequalities and application |
| Citation: | INEQUALITIES FOR CERTAIN POWERS OF POSITIVE DEFINITE MATRICES |
| Series/Report no.: | MIA;doi:10.7153/mia-20-02 |
| Abstract: | Abstract. We give several matrix versions of the inequalities a^b + b^a > 1 and a^a > e^(−e^−1) for positive scalars a and b. For instance, for all positive definite matrices A,B, any Hermitian matrix X, and any unitarily invariant norm, |||A^bX +XB^a|||>=|||X||| ,where a and b are the smallest eigenvalues of A and B, respectively |
| Description: | Mathematics subject classification (2010): 15A18, 15A42, 15A45, 15A60, 26C10. Keywords and phrases: Convex function, Hermitian matrix, positive semidefinite matrix, positive definite matrix, singular value, unitarily invariant norm. c , Zagreb Paper MIA-20-02 1 |
| URI: | https://scholar.ptuk.edu.ps/handle/123456789/269 |
| Appears in Collections: | Applied science faculty |
Files in This Item:
| File | Description | Size | Format | |
|---|---|---|---|---|
| Research_119314_Some Inequalities Fo.pdf | Matrix Analysis | 118 kB | Adobe PDF |  View/Open |
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