Generalizing the inequality per \((J_ 2\otimes M)\geq 2^ n[per(M)]^ 2\) (Q1103022)
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scientific article; zbMATH DE number 4051802
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Generalizing the inequality per \((J_ 2\otimes M)\geq 2^ n[per(M)]^ 2\) |
scientific article; zbMATH DE number 4051802 |
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Generalizing the inequality per \((J_ 2\otimes M)\geq 2^ n[per(M)]^ 2\) (English)
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1988
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Let M be an \(n\times n\) positive semidefinite Hermitian matrix and \(W=(w_{ij})\) either a \(2\times 2\) real matrix such that \(w_{11}w_{22}\geq 0\) and \(w_{12}w_{21}\geq 0\) or a \(2\times 2\) Hermitian matrix such that \(w_{11}w_{22}\geq 0\). The author proves that per (W\(\otimes M)\geq (per W)^ n(per M)^ 2\). The cases of equality are discussed.
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permanent
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positive semidefinite Hermitian matrix
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