What is Affine combination?

In mathematics, an affine combination of x1,..., xn is a linear combination

such that

Here, x1,..., xn can be elements of a vector space over a field K, and the coefficients α i {\displaystyle \alpha _{i}} are elements of K.

The elements x1,..., xn can also be points of a Euclidean space, and, more generally, of an affine space over a field K. In this case the α i {\displaystyle \alpha _{i}} are elements of K , and the affine combination is also a point. See Affine space § Affine combinations and barycenter for the definition in this case.