Matrix normal distribution

A matrix normal random variable.

Notes

The mean parameter specifies the mean. The rowcov parameter specifies the among-row covariance matrix. The colcov parameter specifies the among-column covariance matrix.

The covariance matrices specified by rowcov and colcov must be (symmetric) positive definite. If the samples in :math:X are :math:m \times n, then rowcov must be :math:m \times m and colcov must be :math:n \times n. mean must be the same shape as :math:X.

The probability density function is given by:

.. math::

f(X)=(2\pi)^{-\frac{mn}{2}}|U|^{-\frac{n}{2}}|V|^{-\frac{m}{2}}
\exp(-\frac{1}{2}\operatorname{tr}[U^{-1}(X-M)V^{-1}(X-M)^{T}])

where :math:M is the mean, :math:U the among-row covariance matrix, :math:V the among-column covariance matrix.