toqito.matrix_props.is_diagonally_dominant
==========================================

.. py:module:: toqito.matrix_props.is_diagonally_dominant

.. autoapi-nested-parse::

   Checks if the matrix is diagonally dominant.





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

.. py:function:: is_diagonally_dominant(mat, is_strict = True)

   Check if matrix is diagnal dominant (DD) [@WikiDiagDom].

   A matrix is diagonally dominant if the matrix is square
   and if for every row of the matrix, the magnitude of the diagonal entry in a row is greater
   than or equal to the sum of the magnitudes of all the other (non-diagonal) entries in that row.

   .. rubric:: Examples

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

   \[
       A = \begin{pmatrix}
               2 & -1 & 0 \\
               0 & 2 & -1 \\
               0 & -1 & 2
           \end{pmatrix}
   \]

   our function indicates that this is indeed a diagonally dominant matrix.

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

   A = np.array([[2, -1, 0], [0, 2, -1], [0, -1, 2]])

   print(is_diagonally_dominant(A))
   ```

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

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

   is not diagonally dominant.

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

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

   print(is_diagonally_dominant(B))
   ```

   :param mat: Matrix to check.
   :param is_strict: Whether the inequality is strict.

   :returns: Return `True` if matrix is diagnally dominant, and `False` otherwise.