bibkey: linsinnamon2020hadamard authors: Minghua Lin and Gord Sinnamon year: 2020 title: Revisiting a sharpened version of Hadamard’s determinant inequality doi: 10.1016/j.laa.2020.07.032 claim: The introduction states the diagonal-product determinant bound for Hermitian positive definite matrices, with equality if and only if the matrix is diagonal. strata_touched:

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Revisiting a sharpened version of Hadamard’s determinant inequality

Linear Algebra and its Applications 606 (2020), 192-200.

The introduction, equation (1) and its following sentence, states that the determinant of a Hermitian positive definite matrix is at most the product of its diagonal entries, with equality if and only if the matrix is diagonal. This is the classical inequality, recalled by the authors before their sharpening. The integer determinant loss of at least one is an arithmetic corollary of strict inequality, rather than a separate claim of that paper.

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• DOI: https://doi.org/10.1016/j.laa.2020.07.032
• Bibliographic page: https://arxiv.org/abs/2007.13155
• Primary text: https://www.math.uwo.ca/faculty/sinnamon/pdf/Hadamard.pdf
• Checked on 2026-09-08: title, authors, equation (1), and its equality sentence.