Affine span

Remarks

The affine span of $S$ is the set of all affine combinations of finitely many points of $S$. In $\mathbb{R}^3$: the affine span of two distinct points is the line through them. The span of three points that are not on one line is the plane through them. The span of four points that are not in one plane is all of $\mathbb{R}^3$. For each point $p$ of $S$, the affine span is $p + W$, where $W$ is the linear span of the vectors $q - p$ for $q \in S$. Mathlib also defines the affine span of the empty set: it is the empty affine subspace.