Abstract
Hadamard's determinant inequality was refined and generalized by Zhang and Yang in (1997) [11]. Some special cases of the result were rediscovered recently by Rozanski, Witula and Hetmaniok in (2017) [7]. We revisit the result in the case of positive semi-definite 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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