Matrix and operator inequalities (Q2782171)
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scientific article; zbMATH DE number 1727715
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Matrix and operator inequalities |
scientific article; zbMATH DE number 1727715 |
Statements
28 April 2002
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inequality
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traces
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determinants
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positive definite matrices
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linear bounded operators
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Hilbert space
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Matrix and operator inequalities (English)
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Several inequalities concerning traces and determinants of positive definite matrices are proved. An example: if \(A\) and \(B\) are positive definite \(n\times n\) matrices, then NEWLINE\[NEWLINEn\bigl(\det (AB)\bigr)^{m/n} \leq \text{trace} (A^mB^m)NEWLINE\]NEWLINE for every positive integer \(m\). An inequality involving linear bounded operators on a Hilbert space is presented as well.
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