toqito.matrix_props.is_diagonal

toqito.matrix_props.is_diagonal(mat)[source]

Determine if a matrix is diagonal [WikDiag].

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:

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

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

Examples

Consider the following diagonal matrix:

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

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

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

is not diagonal, as shown using toqito.

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

References