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([ 0.18609797,  0.12416167,  0.28230062, -0.93287608]),
array([-0.48238484,  0.72089168,  0.4763625 ,  0.14387088]),
array([-0.66230111,  0.06548609, -0.6711639 , -0.32650855]),
array([ 0.54224502,  0.67868302, -0.49287336,  0.04935131])]

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([0.37621414, 0.92653274]), array([-0.92653274,  0.37621414])]

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]