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 $K^n$, where $K$ is the field of scalars, for example, the real numbers $R$.
I want to build an affine subset/subspace coordinate system $A'↦ A$ from same affine coordinate system $A$. I dont understand if this is works like a inversion injection map (what morphism?) to affine space from which we started