toqito.matrix_props.is_idempotent
=================================

.. py:module:: toqito.matrix_props.is_idempotent

.. autoapi-nested-parse::

   Checks if the matrix is an idempotent matrix.





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

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

   Check if matrix is the idempotent matrix [@WikiIdemPot].

   An *idempotent matrix* is a square matrix, which, when multiplied by itself, yields itself.
   That is, the matrix \(A\) is idempotent if and only if \(A^2 = A\).

   .. rubric:: Examples

   The following is an example of a \(2 x 2\) idempotent matrix:

   \[
       A = \begin{pmatrix}
           3 & -6 \\
           1 & -2
       \end{pmatrix}
   \]

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

   mat = np.array([[3, -6], [1, -2]])

   print(is_idempotent(mat))
   ```


   Alternatively, the following matrix

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

   is not idempotent.

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

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

   print(is_idempotent(mat))
   ```

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

   :returns: Return `True` if matrix is the idempotent matrix, and `False` otherwise.