A note on the arithmetic-geometric-mean inequality for matrices (Q1188414)
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scientific article; zbMATH DE number 40590
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A note on the arithmetic-geometric-mean inequality for matrices |
scientific article; zbMATH DE number 40590 |
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A note on the arithmetic-geometric-mean inequality for matrices (English)
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13 August 1992
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The authors gives a simple proof of the inequality \(||| AA^*X+XBB^*|||\geq 2||| A^*XB|||\), where \(A,B\) and \(X\) are \(n\times n\) matrices and \(|||\cdot|||\) is any unitarily invariant norm. In case of the Schatten p-norm it is proved that if equality holds then \(AA^*X=XBB^*\).
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arithmetic-geometric-mean inequality for matrices
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Schatten \(p\)-norm
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unitarily invariant norm
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