A stronger version of matrix convexity as applied to functions of Hermitian matrices
<p/> <p>A stronger version of matrix convexity, called hyperconvexity is introduced. It is shown that the function <inline-formula><graphic file="1029-242X-1999-260365-i1.gif"/></inline-formula> is hyperconvex on the set of Hermitian matrices <inline-formul...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
1999-01-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | http://www.journalofinequalitiesandapplications.com/content/3/260365 |
| Summary: | <p/> <p>A stronger version of matrix convexity, called hyperconvexity is introduced. It is shown that the function <inline-formula><graphic file="1029-242X-1999-260365-i1.gif"/></inline-formula> is hyperconvex on the set of Hermitian matrices <inline-formula><graphic file="1029-242X-1999-260365-i2.gif"/></inline-formula> and <inline-formula><graphic file="1029-242X-1999-260365-i3.gif"/></inline-formula> is hyperconvex on the set of positive definite Hermitian matrices. The new concept makes it possible to consider weighted averages of matrices of different orders. Proofs use properties of the Fisher information matrix, a fundamental concept of mathematical statistics.</p> |
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| ISSN: | 1025-5834 1029-242X |