:py:mod:`matrix_props.is_symmetric`
===================================

.. py:module:: matrix_props.is_symmetric

.. autoapi-nested-parse::

   Is matrix a symmetric matrix.



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


Functions
~~~~~~~~~

.. autoapisummary::

   matrix_props.is_symmetric.is_symmetric



.. py:function:: is_symmetric(mat, rtol = 1e-05, atol = 1e-08)

   Determine if a matrix is symmetric :cite:`WikiSymMat`.

   The following 3x3 matrix is an example of a symmetric matrix:

   .. math::

       \begin{pmatrix}
           1 & 7 & 3 \\
           7 & 4 & -5 \\
           3 &-5 & 6
       \end{pmatrix}

   .. rubric:: Examples

   Consider the following matrix

   .. math::
       A = \begin{pmatrix}
               1 & 7 & 3 \\
               7 & 4 & -5 \\
               3 & -5 & 6
           \end{pmatrix}

   our function indicates that this is indeed a symmetric matrix.

   >>> from toqito.matrix_props import is_symmetric
   >>> import numpy as np
   >>> A = np.array([[1, 7, 3], [7, 4, -5], [3, -5, 6]])
   >>> is_symmetric(A)
   True

   Alternatively, the following example matrix :math:`B` defined as

   .. math::
       B = \begin{pmatrix}
               1 & 2 \\
               4 & 5
           \end{pmatrix}

   is not symmetric.

   >>> from toqito.matrix_props import is_symmetric
   >>> import numpy as np
   >>> B = np.array([[1, 2], [3, 4]])
   >>> is_symmetric(B)
   False

   .. rubric:: References

   .. bibliography::
       :filter: docname in docnames

   :param mat: The matrix to check.
   :param rtol: The relative tolerance parameter (default 1e-05).
   :param atol: The absolute tolerance parameter (default 1e-08).
   :return: Returns :code:`True` if the matrix is symmetric and :code:`False` otherwise.