rand.random_orthonormal_basis

Generates a random orthonormal basis.

Functions

random_orthonormal_basis(dim[, is_real, seed])

Generate a real random orthonormal basis of given dimension \(d\).

Module Contents

rand.random_orthonormal_basis.random_orthonormal_basis(dim, is_real=False, seed=None)

Generate a real random orthonormal basis of given dimension \(d\).

The basis is generated from the columns of a random unitary matrix of the same dimension as the columns of a unitary matrix typically form an orthonormal basis [1].

Examples

To generate a random orthonormal basis of dimension \(4\),

>>> from toqito.rand import random_orthonormal_basis
>>> random_orthonormal_basis(4, is_real = True) 
[array([0.52188745, 0.4983613 , 0.69049811, 0.04981832]),
array([-0.48670459,  0.58756912, -0.10226756,  0.63829658]),
array([ 0.23965404, -0.58538248,  0.187136  ,  0.75158061]),
array([ 0.658269  ,  0.25243989, -0.69118291,  0.158815  ])]

It is also possible to add a seed for reproducibility.

>>> from toqito.rand import random_orthonormal_basis
>>> random_orthonormal_basis(2, is_real=True, seed=42)
[array([0.66954664, 0.74277002]), array([-0.74277002,  0.66954664])]

References

[1]

Stack Exchange Mathematics. Why do the columns of a unitary matrix form an orthonormal basis? URL: https://math.stackexchange.com/q/1688950.

dim: int

Number of elements in the random orthonormal basis.

seed: int | None

A seed used to instantiate numpy’s random number generator.

Parameters:

  • dim (int)

  • is_real (bool)

  • seed (int | None)

Return type:

list[numpy.ndarray]