matrix_props.is_linearly_independent

Checks if a set of vectors are linearly independent.

Functions

is_linearly_independent(vectors)

Check if set of vectors are linearly independent [1].

Module Contents

matrix_props.is_linearly_independent.is_linearly_independent(vectors)

Check if set of vectors are linearly independent [1].

Examples

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

\[\begin{split}\begin{pmatrix} 1 \\ 0 \\ 1 \end{pmatrix}, \quad \begin{pmatrix} 1 \\ 1 \\ 0 \end{pmatrix}, \quad \text{and} \quad \begin{pmatrix} 0 \\ 0 \\ 1 \end{pmatrix}\end{split}\]

We can see that these are linearly independent:

>>> 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]])
>>> is_linearly_independent([v_1, v_2, v_3])
np.True_

References

[1] (1,2)

Wikipedia. Linear independence. URL: https://en.wikipedia.org/wiki/Linear_independence.

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