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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 $R$.

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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

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