Affine hull

In mathematics, the affine hull of a set S in Euclidean space Rn is the smallest affine set containing S, or equivalently, the intersection of all affine sets containing S. Here, an affine set may be defined as the translation of a vector subspace.

The affine hull aff(S) of S is the set of all affine combinations of elements of S, that is,

\operatorname{aff} (S)=\left\{\sum_{i=1}^k \alpha_i x_i \, \Bigg | \, k>0, \, x_i\in S, \, \alpha_i\in \mathbb{R}, \, \sum_{i=1}^k \alpha_i=1 \right\}.



Related sets


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