toqito.matrix_props.is_unitary
==============================

.. py:module:: toqito.matrix_props.is_unitary

.. autoapi-nested-parse::

   Checks if the matrix is a unitary matrix.





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

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

   Check if matrix is unitary [@WikiUniMat].

   A matrix is unitary if its inverse is equal to its conjugate transpose.

   Alternatively, a complex square matrix \(U\) is unitary if its conjugate transpose
   \(U^*\) is also its inverse, that is, if

   \[
       \begin{equation}
           U^* U = U U^* = \mathbb{I},
       \end{equation}
   \]

   where \(\mathbb{I}\) is the identity matrix.

   .. rubric:: Examples

   Consider the following matrix

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

   our function indicates that this is indeed a unitary matrix.

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

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

   print(is_unitary(A))
   ```

   We may also use the `random_unitary` function from `toqito`, and can verify that a randomly
   generated matrix is unitary

   ```python exec="1" source="above"
   from toqito.matrix_props import is_unitary
   from toqito.rand import random_unitary

   mat = random_unitary(2)

   print(is_unitary(mat))
   ```

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

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

   is not unitary.

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

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

   print(is_unitary(B))
   ```

   :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 unitary, and `False` otherwise.