Affine combination

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In mathematics, an affine combination of vectors x₁, ..., x_n is vector

called the linear combination of x₁, ..., x_n , 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 α_i 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).

Contents 1 See also 1.1 Related combinations 1.2 Affine geometry 2 References

[edit] See also

[edit] Related combinations

• Convex combination
• Conical combination
• Linear combination

[edit] Affine geometry

• Affine space
• Affine geometry
• Affine hull

[edit] References

• Gallier, Jean (2001), Geometric Methods and Applications, Berlin, New York: Springer-Verlag, ISBN 978-0-387-95044-0 . See chapter 2.