Definition
The probability density function for the random matrix X (n × p) that follows the matrix normal distribution has the form:
where M is n × p, Ω is p × p and Σ is n × n. There are several ways to define the two covariance matrices. One possibility is
where c is a constant which depends on Σ and ensures appropriate power normalization.
The matrix normal is related to the multivariate normal distribution in the following way:
if and only if
where denotes the Kronecker product and denotes the vectorization of .
Read more about this topic: Matrix Normal Distribution
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