In this note, we give a counterexample to show that Hadamard's inequality does not hold on a polyhedron in multi-dimensional Euclidean space. Then we give a sufficient condition on the polyhedron for Hadamard's inequality to hold. Finally, we provide an approach to create a large class of polyhedra on which Hadamard's inequality is true. © 2007 Elsevier Ltd. All rights reserved.
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