Orthogonal affine coordinate systems are rectangular, and others are referred to as oblique.

Basis vectors that are the same at all points are global bases, and can be associated only with linear or affine coordinate systems.

A collection of n affinely independent affine functions is an affine coordinate system on A.

For defining a polynomial function over the affine space, one has to choose an affine coordinate system.

Hence, the abovementioned formulas for Cartesian coordinates are applicable in any affine coordinate system.

An affine coordinate system on A sets up a bijection of A with the complex coordinate space , whose elements are n-tuples of complex numbers.

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.

More precisely, the choice of an affine coordinate system (or, in the real case, a Cartesian coordinate system) for an affine plane P over a field F induces an isomorphism of affine planes between P and F.