Affine subspace/Affine generating system/Definition

Affine generating system

Let $E$ be an affine space over the $K$-vector space $V$, and let $F\subseteq E$ be an affine subspace. A family of points $P_i\in F$, $i\in I$, is called an affine generating system of $F$, if $F$ is the smallest affine subspace of $E$ containing all points $P_i$.