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Hadamard's inequality follows immediately from inspection of both sides of the entropy inequalityh(X₁, X₂,, ⋯, Xₙ)≤ ∑ h(Xᵢ), when(Xₗ, X₂,⋯, Xₙ)is multivariate normal.
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Cover et al. (1983) studied this question.
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