= Affine hull
{title2=$\operatorname{aff}(S)=a+\operatorname{span}\{s-a:s\in S\}$}
{wiki}
= Affine span
{synonym}
The smallest <affine subspace> containing a nonempty set $S$. For any chosen $a\in S$, the displayed formula proves existence and minimality: every containing affine subspace must contain all the indicated differences in its direction space. Equivalently it consists of finite affine combinations $\sum_i\lambda_i s_i$ with $\sum_i\lambda_i=1$. Its dimension can be smaller than the dimension of an affine hyperplane in which the set has been embedded.
Back to article page
