Reverse forms of a convex matrix inequality (Q1893096)
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scientific article; zbMATH DE number 769034
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Reverse forms of a convex matrix inequality |
scientific article; zbMATH DE number 769034 |
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Reverse forms of a convex matrix inequality (English)
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3 July 1995
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Let \(A\) and \(B\) be two complex Hermitian positive definite matrices, and let \(0\leq \lambda\leq 1\). Then \[ [\lambda A+ (1-\lambda) B]^{-1}\leq \lambda A^{-1}+(1-\lambda) B^{-1},\tag{1} \] where \(A\geq B\) means that \(A-B\) is a positive semidefinite matrix. The authors prove two reverse forms of (1) up to a multiplicative constant.
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convex matrix inequality
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complex Hermitian positive definite matrices
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