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Let be a Vector Space over a Field
, and let
be a nonempty Set. Now define addition
for any Vector
and element
subject to the conditions
In an affine space, it is possible to fix a point and coordinate axis such that every point in the Space can be
represented as an -tuple of its coordinates. Every ordered pair of points
and
in an affine space is then
associated with a Vector
.
See also Affine Complex Plane, Affine Connection, Affine Equation, Affine Geometry, Affine Group, Affine Hull, Affine Plane, Affine Space, Affine Transformation, Affinity