Convex combination

Summary

A convex combination of finitely many points is a weighted sum of the points whose weights are nonnegative and add up to $1$. It is the special kind of affine combination in which no weight is negative. The convex hull of a set is exactly the set of all convex combinations of its points. A convex set is a set closed under convex combinations. So convex combinations are the basic operation of convex geometry.