toqito.matrix_props.is_positive_semidefinite

Checks if the matrix is a positive semidefinite matrix.

Module Contents

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

Check if matrix is positive semidefinite (PSD) [@WikiPosDef].

Examples

Consider the following matrix

[

A = begin{pmatrix}

1 & -1 \ -1 & 1

end{pmatrix}

]

our function indicates that this is indeed a positive semidefinite matrix.

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

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

print(is_positive_semidefinite(A)) ```

Alternatively, the following example matrix (B) defined as

[

B = begin{pmatrix}

-1 & -1 \ -1 & -1

end{pmatrix}

]

is not positive semidefinite.

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

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

print(is_positive_semidefinite(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 PSD, and False otherwise.

Return type:

bool