matrix_ops.vectors_to_gram_matrix¶

Calculates the Gram matrix from a list of vectors.

Functions¶

vectors_to_gram_matrix(vectors)

Construct the Gram matrix from a list of vectors [1].

Module Contents¶

matrix_ops.vectors_to_gram_matrix.vectors_to_gram_matrix(vectors)¶

Construct the Gram matrix from a list of vectors [1].

The Gram matrix is a matrix of inner products, where the entry G[i, j] is the inner product of vectors[i] and vectors[j]. This function computes the Gram matrix for a given list of vectors.

Examples

Example with real vectors:

import numpy as np
from toqito.matrix_ops import vectors_to_gram_matrix

vectors = [np.array([1, 2]), np.array([3, 4])]
gram_matrix = vectors_to_gram_matrix(vectors)

gram_matrix

array([[ 5, 11],
       [11, 25]])

Example with complex vectors:

import numpy as np
from toqito.matrix_ops import vectors_to_gram_matrix

vectors = [np.array([1+1j, 2+2j]), np.array([3+3j, 4+4j])]
gram_matrix = vectors_to_gram_matrix(vectors)

gram_matrix

array([[10.+0.j, 22.+0.j],
       [22.+0.j, 50.+0.j]])

References

Raises:: ValueError – If the vectors are not all of the same length.
Parameters:: vectors (list[numpy.ndarray]) – A list of vectors (1D numpy arrays). All vectors must be of the same length.
Returns:: A list of vectors corresponding to the ensemble of states.
Return type:: numpy.ndarray