Wolfram Language & System 11.0 (2016)|Legacy Documentation

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GaussianOrthogonalMatrixDistribution

GaussianOrthogonalMatrixDistribution[σ,n]
represents a Gaussian orthogonal matrix distribution with matrix dimensions {n,n} and scale parameter σ.

GaussianOrthogonalMatrixDistribution[n]
represents a Gaussian orthogonal matrix distribution with unit scale parameter.

DetailsDetails

Background & Context
Background & Context

ExamplesExamplesopen allclose all

Basic Examples  (3)Basic Examples  (3)

Generate a pseudorandom matrix from GOE:

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Check that it is symmetric:

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The entries of a matrix drawn from GaussianOrthogonalMatrixDistribution are jointly Gaussian and uncorrelated, with entries off the diagonal having half the variance of entries on the diagonal:

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Use MatrixPropertyDistribution to sample eigenvalues of GOE matrices:

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Introduced in 2015
(10.3)