In convex geometry, a **convex combination** is a linear combination of points (which can be vectors, scalars, or more generally points in an affine space) where all coefficients are non-negative and sum to 1.

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More formally, given a finite number of points

where the real numbers

As a particular example, every convex combination of two points lies on the line segment between the points.

The convex hull of the given points is identical to the set of all their convex combinations.

There exist subsets of a vector space that are not closed under linear combinations but are closed under convex combinations. For example, the interval