GaussianUnitaryMatrixDistribution

GaussianUnitaryMatrixDistribution[σ,n]

represents a Gaussian unitary matrix distribution with matrix dimensions {n,n} and scale parameter σ.

GaussianUnitaryMatrixDistribution[n]

represents a Gaussian unitary matrix distribution with unit scale parameter.

Details

Background & Context

Examples

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Basic Examples  (4)

Generate a pseudorandom GUE matrix:

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Check that it is Hermitian:

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Independent real components of a matrix from GaussianUnitaryMatrixDistribution are jointly Gaussian, 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 GUE matrices:

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Mean and variance:

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Scope  (4)

Applications  (3)

Properties & Relations  (4)

See Also

NormalDistribution  GaussianOrthogonalMatrixDistribution  GaussianSymplecticMatrixDistribution  MatrixPropertyDistribution  MatrixNormalDistribution  UnitaryMatrixQ

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