Affine coordinate system
In mathematics, an affine coordinate system is a coordinate system on an affine space where each coordinate is an affine map to the number line. In other words, it is an injective affine map from an affine space A to the coordinate space Kn, where K is the field of scalars, for example, the real numbers R.
The most important case of affine coordinates in Euclidean spaces is real-valued Cartesian coordinate system. Orthogonal affine coordinate systems are rectangular, and others are referred to as oblique.
A system of n coordinates on n-dimensional space is defined by a (n+1)-tuple (O, R1, … Rn) of points not belonging to any affine subspace of a lesser dimension. Any given coordinate n-tuple gives the point by the formula:
Note that Rj − O are difference vectors with the origin in O and ends in Rj .
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