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.

Details

Background & Context

Examples

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Basic Examples  (4)

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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Mean and variance:

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Scope  (4)

Applications  (3)

Properties & Relations  (4)

See Also

NormalDistribution  GaussianUnitaryMatrixDistribution  GaussianSymplecticMatrixDistribution  SymmetricMatrixQ

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