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arXiv · 2007.13155

Revisiting a sharpened version of Hadamard's determinant inequality

Minghua Lin·Gord Sinnamon
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Abstract

Hadamard's determinant inequality was refined and generalized by Zhang and Yang in [Acta Math. Appl. Sinica 20 (1997) 269-274]. Some special cases of the result were rediscovered recently by Rozanski, Witula and Hetmaniok in [Linear Algebra Appl. 532 (2017) 500-511]. We revisit the result in the case of positive semidefinite matrices, giving a new proof in terms of majorization and a complete description of the conditions for equality in the positive definite case. We also mention a block extension, which makes use of a result of Thompson in the 1960s.

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BibTeXRIS

Minghua Lin, Gord Sinnamon. 2020-07-26. Revisiting a sharpened version of Hadamard's determinant inequality. https://doi.org/10.1016/j.laa.2020.07.032

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