Let $A$ be an [affine space](/page/Affine%20Space) modeled on a [vector space](/page/Vector%20Space) $V$ over a field $k$. Let $S \subset A$ be nonempty, and let $p_0 \in S$. Then
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\begin{align*}
\operatorname{Aff}(S)=p_0+\operatorname{span}_k\{p-p_0 : p \in S\}.
\end{align*}