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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

Related sets


  1. ^ Roman 2008, p. 430 §16