Affine hull

In mathematics, the affine hull or affine span of a set S in Euclidean space Rn is the smallest affine set containing S,[1] 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, For any subsets,{\displaystyle S,T\subseteq X}
mathematicsEuclidean spaceaffine setintersectiontranslationvector subspaceaffine combinationsempty setsingletonclosed setconvexconvex combinationconvex hullconical combinationconical hulllinear combinationlinear spanRoman, StephenGraduate Texts in Mathematics