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

.. py:module:: matrix_props.is_anti_hermitian

.. autoapi-nested-parse::

   Checks if the matrix is an anti-Hermitian matrix.



Functions
---------

.. autoapisummary::

   matrix_props.is_anti_hermitian.is_anti_hermitian


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) :cite:`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:

   .. math::
       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

   .. math::
       A = -A^*.

   >>> from toqito.matrix_props import is_anti_hermitian
   >>> import numpy as np
   >>> mat = np.array([[2j, -1 + 2j, 4j], [1 + 2j, 3j, -1], [4j, 1, 1j]])
   >>> is_anti_hermitian(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 anti-Hermitian.

   >>> from toqito.matrix_props import is_anti_hermitian
   >>> import numpy as np
   >>> mat = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
   >>> is_anti_hermitian(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 True if matrix is anti-Hermitian, and False otherwise.