Matrix normal distribution
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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 × 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.