toqito.matrix_props.is_diagonally_dominant

Checks if the matrix is diagonally dominant.

Module Contents

toqito.matrix_props.is_diagonally_dominant.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.

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)) ```

Parameters:

• mat (numpy.ndarray) – Matrix to check.

• is_strict (bool) – Whether the inequality is strict.

Returns:

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

Return type:

bool