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

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 .

See also

eo:Vikipedio:Projekto matematiko/Matrica normala distribuo


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