:py:mod:`matrix_ops.vectors_to_gram_matrix`
===========================================

.. py:module:: matrix_ops.vectors_to_gram_matrix

.. autoapi-nested-parse::

   Gram matrix from list of vectors.



Module Contents
---------------


Functions
~~~~~~~~~

.. autoapisummary::

   matrix_ops.vectors_to_gram_matrix.vectors_to_gram_matrix



.. py:function:: vectors_to_gram_matrix(vectors)

   Construct the Gram matrix from a list of vectors :cite:`WikiGram`.

   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.

   .. rubric:: 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]])


   .. rubric:: References

   .. bibliography::
       :filter: docname in docnames

   :raises ValueError: If the vectors are not all of the same length.
   :param vectors: A list of vectors (1D numpy arrays). All vectors must be of the same length.
   :return: A list of vectors corresponding to the ensemble of states.