Euclidean Affine Linear Geometry

Abstract

In the previous chapter we have dealt with the (real and linear) affine space $\mathbb A^n$ as modelled on the vector space $\mathbb R^n$. In this chapter we study the additional structures on $\mathbb A^n$ that come when passing from $\mathbb R^n$ to the euclidean space $E^n$ (see the Chap. 3). Taking into account the scalar product allows one to introduce metric notions (such as distances and angles) into an affine space.