Cours 5 Agreg interne: Dualité 1

We begin by discussing what is called the dual, but above all, duality (in finite dimension). We first show a table that transforms an object of linear algebra into a "dual" object. Then, we define the "dual basis" in finite dimension, we write two formulas that will prove very useful later, and we provide a counterexample in infinite dimension, where the "dual family" of a basis is not a basis (it is in fact only free but not generating).