MatrixNormalDistribution

MatrixNormalDistribution[Σrow,Σcol]

represents zero mean matrix normal distribution with row covariance matrix Σrow and column covariance matrix Σcol.

MatrixNormalDistribution[μ,Σrow,Σcol]

represents matrix normal distribution with mean matrix μ.

Details • MatrixNormalDistribution is a distribution of μ+ .x. , where is a matrix with independent identically distributed matrix elements that follow NormalDistribution[0,1].
• The probability density for a matrix in a matrix normal distribution is proportional to .
• MatrixNormalDistribution[μ,c Σrow,c-1 Σcol] has the same distribution as MatrixNormalDistribution[μ,Σrow,Σcol] for any positive real constant c.
• The covariance matrices Σrow and Σcol can be any symmetric positive definite matrices of real numbers of dimensions {n,n} and {m,m}, respectively, and the mean matrix μ can be any matrix of real numbers of dimensions {n,m}.
• MatrixNormalDistribution can be used with such functions as MatrixPropertyDistribution, EstimatedDistribution, and RandomVariate.

Examples

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Basic Examples(2)

Sample from matrix normal distribution:

 In:= Out= Mean and variance:

 In:= Out//MatrixForm= In:= Out//MatrixForm= Possible Issues(1)

Introduced in 2015
(10.3)
|
Updated in 2017
(11.1)