toqito.matrix_props.is_normal
=============================

.. py:module:: toqito.matrix_props.is_normal

.. autoapi-nested-parse::

   Checks if the matrix is a normal matrix.





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

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

   Determine if a matrix is normal [@WikiNorm].

   A matrix is normal if it commutes with its adjoint

   \[
       \begin{equation}
           [X, X^*] = 0,
       \end{equation}
   \]

   or, equivalently if

   \[
       \begin{equation}
           X^* X = X X^*
       \end{equation}.
   \]

   .. rubric:: Examples

   Consider the following matrix

   \[
       A = \begin{pmatrix}
               1 & 0 & 0 & 0 \\
               0 & 1 & 0 & 0 \\
               0 & 0 & 1 & 0 \\
               0 & 0 & 0 & 1
           \end{pmatrix}
   \]

   our function indicates that this is indeed a normal matrix.

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

   A = np.identity(4)

   print(is_normal(A))
   ```

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

   \[
       B = \begin{pmatrix}
               1 & 2 & 3 \\
               4 & 5 & 6 \\
               7 & 8 & 9
           \end{pmatrix}
   \]

   is not normal.

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

   B = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])

   print(is_normal(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 normal and `False` otherwise.