matrix normal distribution について

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In statistics, the matrix normal distribution is a probability distribution that is a generalization of the multivariate normal distribution to matrix-valued random variables.
== Definition ==
The probability density function for the random matrix X (''n'' × ''p'') that follows the matrix normal distribution

\mathcal_(\mathbf, \mathbf, \mathbf)

has the form:
:

) \right)}|^ |\mathbf|^}

where

\mathrm

denotes trace and M is ''n'' × ''p'', U is ''n'' × ''n'' and V is ''p'' × ''p''.
The matrix normal is related to the multivariate normal distribution in the following way:
:

\mathbf \sim \mathcal_(\mathbf, \mathbf, \mathbf),

if and only if
:

\mathrm(\mathbf) \sim \mathcal_(\mathrm(\mathbf), \mathbf \otimes \mathbf)

where

\otimes

denotes the Kronecker product and

\mathrm(\mathbf)

denotes the vectorization of

\mathbf

.

抄文引用元・出典: フリー百科事典『ウィキペディア（Wikipedia）』
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