:py:mod:`matrix_props.is_diagonal`
==================================

.. py:module:: matrix_props.is_diagonal

.. autoapi-nested-parse::

   Is matrix a diagonal matrix.



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


Functions
~~~~~~~~~

.. autoapisummary::

   matrix_props.is_diagonal.is_diagonal



.. py:function:: is_diagonal(mat)

   Determine if a matrix is diagonal :cite:`WikiDiag`.

   A matrix is diagonal if the matrix is square and if the diagonal of the matrix is non-zero,
   while the off-diagonal elements are all zero.

   The following is an example of a 3-by-3 diagonal matrix:

   .. math::
       \begin{equation}
           \begin{pmatrix}
               1 & 0 & 0 \\
               0 & 2 & 0 \\
               0 & 0 & 3
           \end{pmatrix}
       \end{equation}

   This quick implementation is given by Daniel F. from StackOverflow in :cite:`SO_43884189`.

   .. rubric:: Examples

   Consider the following diagonal matrix:

   .. math::
       A = \begin{pmatrix}
               1 & 0 \\
               0 & 1
           \end{pmatrix}.

   Our function indicates that this is indeed a diagonal matrix:

   >>> from toqito.matrix_props import is_diagonal
   >>> import numpy as np
   >>> A = np.array([[1, 0], [0, 1]])
   >>> is_diagonal(A)
   True

   Alternatively, the following example matrix

   .. math::
       B = \begin{pmatrix}
               1 & 2 \\
               3 & 4
           \end{pmatrix}

   is not diagonal, as shown using :code:`toqito`.

   >>> from toqito.matrix_props import is_diagonal
   >>> import numpy as np
   >>> B = np.array([[1, 2], [3, 4]])
   >>> is_diagonal(B)
   False

   .. rubric:: References

   .. bibliography::
       :filter: docname in docnames

   :param mat: The matrix to check.
   :return: Returns :code:`True` if the matrix is diagonal
            and :code:`False` otherwise.