On a matrix inequality (Q1087961)
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scientific article; zbMATH DE number 3989565
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On a matrix inequality |
scientific article; zbMATH DE number 3989565 |
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On a matrix inequality (English)
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1987
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S\({}_ n\) is the set of all real symmetric matrices and \(\Pi_ n\subset S_ n\) the set of symmetric projections. For \(n\geq 1\) the real functions f with f(PAP)\(\leq Pf(A)P\) for all \(A\in S_ n\) and \(P\in \Pi_ n\) are precisely the matrix-convex functions on \(S_ n\) [meaning: \(f(1/2(B+C))\leq 1/2(f(B)+f(C))\) for all \(B,C\in S_ n]\) with f(0)\(\leq 0\).
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matrix inequality
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real symmetric matrices
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symmetric projections
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matrix-convex functions
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