toqito.matrix_props.is_projection

Checks if the matrix is a projection matrix.

Module Contents

toqito.matrix_props.is_projection.is_projection(mat, rtol=1e-05, atol=1e-08)

Check if matrix is a projection matrix [@WikiProjMat].

A matrix is a projection matrix if it is positive semidefinite (PSD) and if

[

begin{equation}

X^2 = X

end{equation}

]

where (X) is the matrix in question.

Examples

Consider the following matrix

[

A = begin{pmatrix}

0 & 1 \ 0 & 1

end{pmatrix}

]

our function indicates that this is indeed a projection matrix.

```python exec=”1” source=”above” import numpy as np from toqito.matrix_props import is_projection

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

print(is_projection(A)) ```

Alternatively, the following example matrix (B) defined as

[

B = begin{pmatrix}

-1 & -1 \ -1 & -1

end{pmatrix}

]

is not positive definite.

```python exec=”1” source=”above” import numpy as np from toqito.matrix_props import is_projection

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

print(is_projection(B)) ```

Parameters:

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

• rtol (float) – The relative tolerance parameter (default 1e-05).

• atol (float) – The absolute tolerance parameter (default 1e-08).

Returns:

Return True if matrix is a projection matrix, and False otherwise.

Return type:

bool