Notes on the arithmetic-geometric mean inequality (Q6657286)
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scientific article; zbMATH DE number 7962141
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Notes on the arithmetic-geometric mean inequality |
scientific article; zbMATH DE number 7962141 |
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Notes on the arithmetic-geometric mean inequality (English)
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6 January 2025
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Starting with the scalar inequality \N\[\N|(ab)^{1/2}x+(ab)^{-1/2}y|\le \frac{|ax + b^{-1}y|+|bx + a^{-1}y|}{2},\N\]\Nwhere \(a, b\) are positive real numbers and \(x, y\) are complex numbers, the authors present matrix versions of it and some generalizations.
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arithmetic-geometric mean inequality
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positive definite matrix
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unitarily invariant norm
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Poisson integral formula
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Hadamard product
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