:py:mod:`matrix_props.is_identity`
==================================

.. py:module:: matrix_props.is_identity

.. autoapi-nested-parse::

   Is matrix the identity matrix.



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


Functions
~~~~~~~~~

.. autoapisummary::

   matrix_props.is_identity.is_identity



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

   Check if matrix is the identity matrix :cite:`WikiIden`.

   For dimension :math:`n`, the :math:`n \times n` identity matrix is defined as

   .. math::
       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:

   .. math::
       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.

   >>> from toqito.matrix_props import is_identity
   >>> import numpy as np
   >>> mat = np.eye(3)
   >>> is_identity(mat)
   True

   Alternatively, the following example matrix :math:`B` defined as

   .. math::
       B = \begin{pmatrix}
               1 & 2 & 3 \\
               4 & 5 & 6 \\
               7 & 8 & 9
           \end{pmatrix}

   is not an identity matrix.

   >>> from toqito.matrix_props import is_identity
   >>> import numpy as np
   >>> mat = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
   >>> is_identity(mat)
   False

   .. rubric:: References

   .. bibliography::
       :filter: docname in docnames

   :param mat: Matrix to check.
   :param rtol: The relative tolerance parameter (default 1e-05).
   :param atol: The absolute tolerance parameter (default 1e-08).
   :return: Return :code:`True` if matrix is the identity matrix, and
           :code:`False` otherwise.