1. Notion of metric

1.1 Introduction

The metric represents the measure of the unit in all directions. The usual metric is the Euclidean metric, for which the measure of the unit in all directions is equal to one. To define a metric, we need to define the notion of length or, more precisely, the norm of a vector. The latter is linked to the notion of the scalar product of two vectors. The usual scalar product is associated with the Pythagorean theorem:

which characterizes a right-angled...