Linear Applications and Matrices

This lecture explores the bijection between linear applications and matrices, defining the operations on the space of linear applications and showing the bijectivity. It covers the proof of linearity, injectivity, and surjectivity, leading to the conclusion that the null application is the neutral element. The lecture also discusses the consequences of this bijection, such as the dimension equivalence between the space of linear applications and matrices. Various propositions and proofs are presented to illustrate the concepts, including the equality of matrices under specific conditions. The use of canonical bases and linear transformations is emphasized throughout the lecture.