Chebyshev type inequalities involving permanents and their applications. (English) Zbl 1117.15020
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\()/(\prod^{n}_i{}_={}_1 \sum^{n}_j{}_={}_1b{}_i{}_,{}_j)\).
Reviewer: Mihail Voicu (Iaşi)
MSC:
| 15A45 | Miscellaneous inequalities involving matrices |
| 15A15 | Determinants, permanents, traces, other special matrix functions |
References:
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