Chebyshev type inequalities involving permanents and their applications (Q869941)
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scientific article; zbMATH DE number 5132633
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Chebyshev type inequalities involving permanents and their applications |
scientific article; zbMATH DE number 5132633 |
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Chebyshev type inequalities involving permanents and their applications (English)
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9 March 2007
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Given the matrices \(A=(a{}_i{}_,{}_j){}_m{}_\times{}_n, B=(b{}_i{}_,{}_j){}_m{}_\times{}_n\), under adequate hypotheses, it is shown that per(\(A^*B)/(n!) \geqslant\) [per\(A/(n!)\)] [per\(B/(n!)\)], where \(A^*B\) denote the Hadamard product of matrices \(A, B\), and (per\(A)/(\prod^{n}_i{}_={}_1\sum^{n}_j{}_={}_1a{}_i{}_,{}_j)\) \(\leqslant (per\)B\()/(\prod^{n}_i{}_={}_1 \sum^{n}_j{}_={}_1b{}_i{}_,{}_j)\).
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