toqito.matrix_props.is_anti_hermitian
=====================================

.. py:module:: toqito.matrix_props.is_anti_hermitian

.. autoapi-nested-parse::

   Checks if the matrix is an anti-Hermitian matrix.





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

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

   Check if matrix is anti-Hermitian (a.k.a. skew-Hermitian) [@WikiAntiHerm].

   An anti-Hermitian matrix is a complex square matrix that is equal to the negative of its own
   conjugate transpose.

   .. rubric:: Examples

   Consider the following matrix:

   \[
       A = \begin{pmatrix}
               2j & -1 + 2j & 4j \\
               1 + 2j & 3j & -1 \\
               4j & 1 & 1j
           \end{pmatrix}
   \]

   our function indicates that this is indeed an anti-Hermitian matrix as it holds that

   \[
       A = -A^*.
   \]

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

   mat = np.array([[2j, -1 + 2j, 4j], [1 + 2j, 3j, -1], [4j, 1, 1j]])

   print(is_anti_hermitian(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 anti-Hermitian.

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

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

   print(is_anti_hermitian(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 anti-Hermitian, and False otherwise.