toqito.matrix_props.is_diagonal

Checks if the matrix is a diagonal matrix.

Module Contents

toqito.matrix_props.is_diagonal.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].

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)) ```

Parameters:

mat (numpy.ndarray) – The matrix to check.

Returns:

Returns True if the matrix is diagonal and False otherwise.

Return type:

bool