ABSTRACT
Euclidean space stripped naked has neither coordinates, nor addition, nor multiplication by scalars, as does R n ; it has only points, lines, planes, etc., and when thought of this way, without any metric or vector space properties, it is referred to as affine space. More precisely, an affine space of dimension n over R is a set E on which the additive group R n operates simply transitively. Thus for each pair of points, P, Q in E there is a unique vector v in R n from Q to P: https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429502408/295d3acc-dfa3-4421-a2d3-a9c22ffb681c/content/pg41_1.tif"/>
