论文标题
重新审视哈达玛德决定因素不平等的锐化版本
Revisiting a sharpened version of Hadamard's determinant inequality
论文作者
论文摘要
张和杨在[acta Math中都通过张和杨进行了完善和概括。应用。 Sinica 20（1997）269-274]。 Rozanski，Witula和Hetmaniok最近在[线性代数应用程序中重新发现了结果的一些特殊情况。 532（2017）500-511]。我们在阳性半限定矩阵的情况下重新审视了结果，从而为大型化和对正定情况下平等条件的完整描述提供了新的证明。我们还提到了一个块扩展，该扩展是利用1960年代汤普森的结果。
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.
