Matrix normal distribution

The matrix normal distribution is a probability distribution that is a generalization of the normal distribution. The probability density function for the random matrix X(N x P) that follows the matrix normal distribution has the form

$p(\mathbf {X} |\mathbf {M} ,{\boldsymbol {\Omega }},{\boldsymbol {\Sigma }})=(2\pi )^{-NP/2}|{\boldsymbol {\Omega }}|^{-P/2}|{\boldsymbol {\Sigma }}|^{-N/2}\exp \left(-{\frac {1}{2}}{\mbox{tr}}\left[{\boldsymbol {\Omega }}^{-1}(\mathbf {X} -\mathbf {M} ){\boldsymbol {\Sigma }}^{-1}(\mathbf {X} -\mathbf {M} )^{T}\right]\right)$