toqito.matrix_props.is_linearly_independent

Checks if a set of vectors are linearly independent.

Module Contents

toqito.matrix_props.is_linearly_independent.is_linearly_independent(vectors)

Check if set of vectors are linearly independent [@WikiLinearIndependence].

Examples

The following vectors are an example of a linearly independent set of vectors in (mathbb{R}^3).

[

begin{pmatrix}

1 \ 0 \ 1

end{pmatrix}, quad begin{pmatrix}

1 \ 1 \ 0

end{pmatrix}, quad text{and} quad begin{pmatrix}

0 \ 0 \ 1

end{pmatrix}

]

We can see that these are linearly independent.

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

v_1 = np.array([[1], [0], [1]]) v_2 = np.array([[1], [1], [0]]) v_3 = np.array([[0], [0], [1]])

print(is_linearly_independent([v_1, v_2, v_3])) ```

Parameters:

vectors (list[numpy.ndarray]) – Vectors to check the linear independence of.

Returns:

Return True if vectors are linearly independent False otherwise.

Return type:

bool