On an inequality for the Hadamard product of an \(M\)-matrix and its inverse (Q1968758)
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scientific article; zbMATH DE number 1419716
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On an inequality for the Hadamard product of an \(M\)-matrix and its inverse |
scientific article; zbMATH DE number 1419716 |
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On an inequality for the Hadamard product of an \(M\)-matrix and its inverse (English)
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22 October 2000
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Let \(A=[a_{jk}]\) be an \(n\times n\) \(M\)-matrix whose inverse is doubly stochastic. Then \[ q(A\circ A^{-1})\geq 2\max a_{kk}/(n \max a_{kk}-n+1), \] where \(\circ\) denotes the Hadamard product, \(q(B)=1/p(B^{-1})\) and \(p(C)\) is the Perron eigenvalue of a nonnegative matrix \(C\).
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doubly stochastic matrix
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Perron eigenvalue
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nonnegative matrix
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\(M\)-matrix
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inequality
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inverse
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Hadamard product
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