toqito.matrix_props.is_symmetric
================================

.. py:module:: toqito.matrix_props.is_symmetric

.. autoapi-nested-parse::

   Checks if the matrix is a symmetric matrix.





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

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

   Determine if a matrix is symmetric [@WikiSymMat].

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

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

   .. rubric:: Examples

   Consider the following matrix

   \[
       A = \begin{pmatrix}
               1 & 7 & 3 \\
               7 & 4 & -5 \\
               3 & -5 & 6
           \end{pmatrix}
   \]

   our function indicates that this is indeed a symmetric matrix.

   ```python exec="1" source="above"
   import numpy as np
   from toqito.matrix_props import is_symmetric

   A = np.array([[1, 7, 3], [7, 4, -5], [3, -5, 6]])

   print(is_symmetric(A))
   ```

   Alternatively, the following example matrix \(B\) defined as

   \[
       B = \begin{pmatrix}
               1 & 2 \\
               4 & 5
           \end{pmatrix}
   \]

   is not symmetric.

   ```python exec="1" source="above"
   import numpy as np
   from toqito.matrix_props import is_symmetric

   B = np.array([[1, 2], [3, 4]])

   print(is_symmetric(B))
   ```

   :param mat: The matrix to check.
   :param rtol: The relative tolerance parameter (default 1e-05).
   :param atol: The absolute tolerance parameter (default 1e-08).

   :returns: Returns `True` if the matrix is symmetric and `False` otherwise.