toqito.matrix_props.is_identity
===============================

.. py:module:: toqito.matrix_props.is_identity

.. autoapi-nested-parse::

   Checks if the matrix is an identity matrix.





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

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

   Check if matrix is the identity matrix [@WikiIden].

   For dimension \(n\), the \(n \times n\) identity matrix is defined as

   \[
       I_n =
       \begin{pmatrix}
           1 & 0 & 0 & \ldots & 0 \\
           0 & 1 & 0 & \ldots & 0 \\
           0 & 0 & 1 & \ldots & 0 \\
           \vdots & \vdots & \vdots & \ddots & \vdots \\
           0 & 0 & 0 & \ldots & 1
       \end{pmatrix}.
   \]

   .. rubric:: Examples

   Consider the following matrix:

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

   our function indicates that this is indeed the identity matrix of dimension
   3.

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

   mat = np.eye(3)

   print(is_identity(mat))
   ```

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

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

   is not an identity matrix.

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

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

   print(is_identity(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 identity matrix, and `False` otherwise.