toqito.matrix_props.is_positive_definite

Checks if the matrix is a positive definite matrix.

Module Contents

toqito.matrix_props.is_positive_definite.is_positive_definite(mat)

Check if matrix is positive definite (PD) [@WikiPosDef].

Examples

Consider the following matrix

[

A = begin{pmatrix}

2 & -1 & 0 \ -1 & 2 & -1 \ 0 & -1 & 2

end{pmatrix}

]

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

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

A = np.array([[2, -1, 0], [-1, 2, -1], [0, -1, 2]])

print(is_positive_definite(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_positive_definite

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

print(is_positive_definite(B)) ```

!!! See Also

[is_positive_semidefinite][toqito.matrix_props.is_positive_semidefinite.is_positive_semidefinite]

Parameters:

mat (numpy.ndarray) – Matrix to check.

Returns:

Return True if matrix is positive definite, and False otherwise.

Return type:

bool