  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.
