Affine Map

up:: Affine Space

An affine transformation is a map which preserves affine structures ─ i.e. it preserves, in particular, “distances” between points in the set (with respect to the associated group action).

A map between affine spaces is said to be an affine transformation if there is a Linear Transformation between their respective vector spaces (which is called the underlying linear map of ) such that

Equivalently, one can say that, for any pair of points , we have that

Properties

• The underlying linear map of an affine map is unique
• An affine map which is bijective is an Affine Isomorphism

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References

• Affine transformation - Wikipedia