toqito.matrix_props.is_diagonal
===============================

.. py:module:: toqito.matrix_props.is_diagonal

.. autoapi-nested-parse::

   Checks if the matrix is a diagonal matrix.





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

.. py:function:: is_diagonal(mat)

   Determine if a matrix is diagonal [@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:

   \[
       \begin{equation}
           \begin{pmatrix}
               1 & 0 & 0 \\
               0 & 2 & 0 \\
               0 & 0 & 3
           \end{pmatrix}
       \end{equation}
   \]

   This quick implementation is given by Daniel F. from StackOverflow in [@SO_43884189].

   .. rubric:: Examples

   Consider the following diagonal matrix:

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

   Our function indicates that this is indeed a diagonal matrix:

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

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

   print(is_diagonal(A))
   ```

   Alternatively, the following example matrix

   \[
       B = \begin{pmatrix}
               1 & 2 \\
               3 & 4
           \end{pmatrix}
   \]

   is not diagonal, as shown using `|toqito⟩`.

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

   B = np.array([[1, 2], [3, 4]])

   print(is_diagonal(B))
   ```

   :param mat: The matrix to check.

   :returns: Returns `True` if the matrix is diagonal and `False` otherwise.