Inequalities for sums of matrix quadratic forms (Q1914243)
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scientific article; zbMATH DE number 885081
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Inequalities for sums of matrix quadratic forms |
scientific article; zbMATH DE number 885081 |
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Inequalities for sums of matrix quadratic forms (English)
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9 October 1996
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This paper proves an inequality for positive definite \(C\) and \(n\times n\) matrices \(U_1, \dots, U_m\) \[ \sum^m_{k=1} (C+ U_1+ \dots+ U_k)^{-1} U_k (C+ U_1+ \dots+ U_k) \leq a_m C^{-1} \] where \(a_m\) is an explicit sequence of rational numbers, which is best possible. The case of powers other than \(-1\) is also discussed.
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positive definite matrix
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sum of matrix quadratic forms
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inequality
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0.9146148
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0.9071603
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0.90266764
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0.89388716
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