Real Affine Hulls
Definition
The affine hull of a set in $n$-dimensional space is the intersection of the collection of affine sets which contain it.
Notation
We denote the affine hull of $S$ by $\aff S$.
The affine hull of $S \subset \R ^n$ consists
of all vectors which can be expressed as
\[ \lambda _1 x_1 + \lambda _2 x_2 \cdots + \lambda _m x_m \]
such that $x_i \in S$ and $\sum_i \lambda _i = 1$.Also, notice that if $A \subset \R ^n$ is affine, then $\aff A = A$.