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...
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SpringerOpen
1999-01-01
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| Series: | Journal of Inequalities and Applications |
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| Online Access: | http://www.journalofinequalitiesandapplications.com/content/3/260365 |
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doaj-79fa6d1d443a4bb19daf39d71ac27edc2020-11-25T00:27:33ZengSpringerOpenJournal of Inequalities and Applications1025-58341029-242X1999-01-0119992260365A stronger version of matrix convexity as applied to functions of Hermitian matricesKagan AbramSmith Paul J<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>http://www.journalofinequalitiesandapplications.com/content/3/260365Matrix convexityHyperconvexityFisher information |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Kagan Abram Smith Paul J |
| spellingShingle |
Kagan Abram Smith Paul J A stronger version of matrix convexity as applied to functions of Hermitian matrices Journal of Inequalities and Applications Matrix convexity Hyperconvexity Fisher information |
| author_facet |
Kagan Abram Smith Paul J |
| author_sort |
Kagan Abram |
| title |
A stronger version of matrix convexity as applied to functions of Hermitian matrices |
| title_short |
A stronger version of matrix convexity as applied to functions of Hermitian matrices |
| title_full |
A stronger version of matrix convexity as applied to functions of Hermitian matrices |
| title_fullStr |
A stronger version of matrix convexity as applied to functions of Hermitian matrices |
| title_full_unstemmed |
A stronger version of matrix convexity as applied to functions of Hermitian matrices |
| title_sort |
stronger version of matrix convexity as applied to functions of hermitian matrices |
| publisher |
SpringerOpen |
| series |
Journal of Inequalities and Applications |
| issn |
1025-5834 1029-242X |
| publishDate |
1999-01-01 |
| description |
<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> |
| topic |
Matrix convexity Hyperconvexity Fisher information |
| url |
http://www.journalofinequalitiesandapplications.com/content/3/260365 |
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