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wiki gives this equation to compute the pdf of the multivariate normal in k dimensions

${\displaystyle f_{\mathbf {X} }(x_{1},\ldots ,x_{k})={\frac {\exp \left(-{\frac {1}{2}}({\mathbf {x} }-{\boldsymbol {\mu }})^{\mathrm {T} }{\boldsymbol {\Sigma }}^{-1}({\mathbf {x} }-{\boldsymbol {\mu }})\right)}{\sqrt {(2\pi )^{k}|{\boldsymbol {\Sigma }}|}}}}$

Some other posts such as this one uses this form

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Is there a detailed mathematical derivation from the latter to the former?

JJJohn
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1 Answers1

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The first one is for a general multivariate normal distribution and the second one is only for independent and identically distributed normal variables.

Kavi Rama Murthy
  • 311,013