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 ${}P_{i}$.