matrix_props.mutual_coherence
=============================

.. py:module:: matrix_props.mutual_coherence

.. autoapi-nested-parse::

   Computes the mutual coherence for a list of 1D numpy arrays.



Functions
---------

.. autoapisummary::

   matrix_props.mutual_coherence.mutual_coherence


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

.. py:function:: mutual_coherence(vectors)

   Calculate the mutual coherence of a collection of input vectors.

   The mutual coherence of a collection of input vectors is defined as the maximum
   absolute value of the inner product between any two distinct vectors, divided by the
   product of their norms :footcite:`WikiMutualCoh`. It provides a measure of how
   similar the vectors are to each other.

   .. rubric:: Examples

   .. jupyter-execute::

       import numpy as np
       from toqito.matrix_props.mutual_coherence import mutual_coherence
       example_A = [np.array([1, 0]), np.array([0, 1])]
       print("Result for example_A = ",mutual_coherence(example_A))
       # An example with a larger set of vectors
       example_B = [np.array([1, 0, 1]), np.array([0, 1, 1]), np.array([1, 1, 0])]
       print("Result for example_B = ",mutual_coherence(example_B))

   .. rubric:: References

   .. footbibliography::

   :param vectors: A list of 1D numpy arrays.
   :raises ValueError: If arrays in list are not 1D.
   :raises TypeError: If input is not a list.
   :return: The mutual coherence of the collection of input vectors.