# Basis of a linear subspace : basis

### 5.47.9 Basis of a linear subspace : basis

The basis command finds a basis of a linear subspace of ℝn given a spanning set.

- basis takes one argument:
  L, a list of vectors generating a linear subspace of ℝn.
- basis(L) returns a list of vectors that is a basis of this linear subspace.

#### Example.

Input:

basis([[1,2,3],[1,1,1],[2,3,4]])

Output:

⎧ ⎨ ⎩ | ⎡ ⎣ | −1,0,1 | ⎤ ⎦ | , | ⎡ ⎣ | 0,−1,−2 | ⎤ ⎦ | ⎫ ⎬ ⎭