In mathematics, an affine combination of vectors x1, ..., xn is vector
called the linear combination of x1, ..., xn , in which the sum of the coefficients is 1, thus:
Here the vectors are elements of a given vector space V over a field K, and the coefficients αi are scalars in K.
This concept is important, for example, in Euclidean geometry.
An affine combination of fixed points of an affine transformation is also a fixed point, so the fixed points form an affine subspace (in 3D: a line or a plane, and the trivial cases, a point and the whole space).
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See also
Related combinations
For more details on this topic, see Linear combination#Affine, conical, and convex combinations.
Affine geometry
References
- Gallier, Jean (2001), Geometric Methods and Applications, Berlin, New York: Springer-Verlag, ISBN 978-0-387-95044-0. See chapter 2.
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