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

<math>

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) <math>

See also Multivariate normal distribution.