Wolfram Language & System 11.0 (2016)|Legacy Documentation

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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:

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Sample from matrix normal distribution with independent rows:

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

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Sample from matrix normal distribution with independent rows:

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

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

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Introduced in 2015
(10.3)