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If X‾=(X1,…,Xn)T∼N(μ‾,KX‾)\underline X=(X_{1},\ldots,X_{n})^{T}\sim\mathcal{N}(\underline\mu,K_{\underline X})X=(X1,…,Xn)T∼N(μ,KX) then h(X‾)=h(X1,…,Xn)=12log2[(2πe)ndet(KX‾)]h(\underline X)=h(X_{1},\ldots,X_{n})=\frac{1}{2}\log_{2}\left[(2\pi e)^{n}\det(K_{\underline X})\right]h(X)=h(X1,…,Xn)=21log2[(2πe)ndet(KX)]
A special case is if n=1n=1n=1, then h(X1)=12log2[(2πe)σ12]h(X_{1})=\frac{1}{2}\log_{2}[(2\pi e)\sigma_{1}^{2}]h(X1)=21log2[(2πe)σ12]where σ12=\mboxVar(X1)\sigma_{1}^{2}=\mbox{Var}(X_{1})σ12=\mboxVar(X1).