TOPICS
Search

Affine Combination

An affine combination of points or vectors x_1, ..., x_n is a linear combination

x=sum_(i=1)^(n)lambda_ix_i
(1)
sum_(i=1)^(n)lambda_i=1.
(2)

The coefficient condition makes affine combinations independent of the choice of origin. The set of all affine combinations of a collection of points is its affine hull. If the coefficients are also nonnegative, the combination is a convex combination, and the set of all such combinations is the convex hull.

See also

Affine Hull, Affine Space, Barycentric Coordinates, Convex Combination, Convex Hull, Linear Combination, Vector

Explore with Wolfram|Alpha

References

Boyd, S. and Vandenberghe, L. "Affine Sets." §2.1.1 in Convex Optimization. Cambridge, England: Cambridge University Press, pp. 21-23, 2004. https://web.stanford.edu/~boyd/cvxbook/.

Cite this as:

Weisstein, Eric W. "Affine Combination." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/AffineCombination.html

Subject classifications