A subset of a vector space is said to be convex if for all vectors , and all scalars . Via induction, this can be seen to be equivalent to the requirement that for all vectors , and for all scalars such that . With the above restrictions on the , an expression of the form is said to be a convex combination of the vectors .

The set of all convex combinations of vectors in constitute the convex hull of so, for example, if are two different vectors in the vector space , then the set of all convex combinations of and constitute the line segment between and .