# Wolfram Language & System 11.0 (2016)|Legacy Documentation

This is documentation for an earlier version of the Wolfram Language.
BUILT-IN WOLFRAM LANGUAGE SYMBOL

# 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.

## DetailsDetails

• 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 .
• 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 RandomVariate and MatrixPropertyDistribution.

## ExamplesExamplesopen allclose all

### Basic Examples  (3)Basic Examples  (3)

Sample from matrix normal distribution:

 In[1]:=
 Out[1]=

Sample from matrix normal distribution with independent rows:

 In[1]:=

Test the hypothesis that rows follow multinormal distribution with the column covariance matrix:

 In[2]:=
 Out[2]=

Sample from matrix normal distribution with independent rows:

 In[1]:=

Computing sample inter-row covariances shows different rows are pairwise independent:

 In[2]:=
 Out[2]//MatrixForm=

Computing sample inter-column covariances shows different columns are dependent:

 In[3]:=
 Out[3]//MatrixForm=

## See AlsoSee Also

Introduced in 2015
(10.3)