toqito.matrix_props.is_permutation
==================================

.. py:module:: toqito.matrix_props.is_permutation

.. autoapi-nested-parse::

   Checks if the matrix is a permutation matrix.





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

.. py:function:: is_permutation(mat)

   Determine if a matrix is a permutation matrix [@WikiPerm].

   A matrix is a permutation matrix if each row and column has a
   single element of 1 and all others are 0.

   .. rubric:: Examples

   Consider the following permutation matrix

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

   which is indeed a permutation matrix.

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

   A = np.array([[1, 0, 0], [0, 0, 1], [0, 1, 0]])

   print(is_permutation(A))
   ```


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

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

   has 2 columns with all zero values and is thus not a
   permutation matrix.

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

   B = np.array([[1, 0, 0], [1, 0, 0], [1, 0, 0]])

   print(is_permutation(B))
   ```

   :param mat: The matrix to check.

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