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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. More formally, given a finite number of points in a real vector space, a convex combination of these points is a point of the form where the real numbers satisfy and As a particular example, every convex combination of two points lies on the line segment between the points.

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• Convex combination
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• 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. More formally, given a finite number of points in a real vector space, a convex combination of these points is a point of the form where the real numbers satisfy and As a particular example, every convex combination of two points lies on the line segment between the points.
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• 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. More formally, given a finite number of points in a real vector space, a convex combination of these points is a point of the form where the real numbers satisfy and As a particular example, every convex combination of two points lies on the line segment between the points. A set is convex if it contains all convex combinations of its points.The convex hull of a given set of 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 is convex but generates the real-number line under linear combinations. Another example is the convex set of probability distributions, as linear combinations preserve neither nonnegativity nor affinity (i.e., having total integral one).
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