Chollet's permanent conjecture for 4 × 4 matrices (Q6638360)
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scientific article; zbMATH DE number 7944386
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Chollet's permanent conjecture for 4 × 4 matrices |
scientific article; zbMATH DE number 7944386 |
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Chollet's permanent conjecture for 4 × 4 matrices (English)
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14 November 2024
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Let \(A,B\in\mathbb{C}^{n\times n}\) be nonnegative definite, and let \(\circ\) denote the Hadamard product. \textit{J. Chollet} [Am. Math. Mon. 89, 57--58 (1982; Zbl 0507.15004)] conjectured that\N\[\N\operatorname{per}{A}\,\operatorname{per}{B}\ge\operatorname{per}(A\circ B).\N\]\NThis conjecture has already been proved for \(n\le 3\), and also for \(n=4\) in the case of real matrices. The author proves it for \(n=4\) in general.
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