matrix_ops.vectors_to_gram_matrix
=================================

.. py:module:: matrix_ops.vectors_to_gram_matrix

.. autoapi-nested-parse::

   Calculates the Gram matrix from a list of vectors.



Functions
---------

.. autoapisummary::

   matrix_ops.vectors_to_gram_matrix.vectors_to_gram_matrix


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

.. 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:

   .. jupyter-execute::

    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

   Example with complex vectors:

   .. jupyter-execute::

    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

   .. 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.