:py:mod:`matrix_props.is_linearly_independent`
==============================================

.. py:module:: matrix_props.is_linearly_independent

.. autoapi-nested-parse::

   Is linearly independent.



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


Functions
~~~~~~~~~

.. autoapisummary::

   matrix_props.is_linearly_independent.is_linearly_independent



.. py:function:: is_linearly_independent(vectors)

   Check if set of vectors are linearly independent :cite:`WikiLinearIndependence`.

   .. rubric:: Examples

   The following vectors are an example of a linearly independent set of vectors in :math:`\mathbb{R}^3`.

   .. math::
       \begin{pmatrix}
           1 \\ 0 \\ 1
       \end{pmatrix}, \quad
       \begin{pmatrix}
           1 \\ 1 \\ 0
       \end{pmatrix}, \quad \text{and} \quad
       \begin{pmatrix}
           0 \\ 0 \\ 1
       \end{pmatrix}

   We can see that these are linearly independent:

   >>> import numpy as np
   >>> from toqito.matrix_props import is_linearly_independent
   >>>
   >>> v_1 = np.array([[1], [0], [1]])
   >>> v_2 = np.array([[1], [1], [0]])
   >>> v_3 = np.array([[0], [0], [1]])
   >>> is_linearly_independent([v_1, v_2, v_3])
   True

   .. rubric:: References

   .. bibliography::
       :filter: docname in docnames

   :param vectors: Vectors to check the linear independence of.
   :return: Return :code:`True` if vectors are linearly independent :code:`False` otherwise.