Convex combination
In convex geometry and vector algebra, 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. In other words, the operation is equivalent to a standard weighted average, but whose weights are expressed as a percent of the total weight, instead of as a fraction of the count of the weights as in a standard weighted average.
Convex combination - Wikipedia Jump to content From Wikipedia, the free encyclopedia Linear combination of points where all coefficients are non-negative and sum to 1 Given three points x 1 , x 2 , x 3 {\displaystyle x_{1},x_{2},x_{3}} in a plane as shown in the figure, the point P {\displaystyle P} is a convex combination of the three points, while Q {\displaystyle Q} is not . ( Q {\displaystyle Q} is however an affine combination of the three points, as their affine hull is the entire plane.) Convex combination of two points v 1 , v 2 ∈ R 2 {\displaystyle v_{1},v_{2}\in \mathbb {R} ^{2}} in
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