Linear Algebra: Compositions of Applications

This lecture covers the concept of compositions of applications in linear algebra, where the composed maps f: E -> F and g: F -> G are defined. The lecture explains the definition of the composition g o f: E -> G, illustrating examples and discussing the injectivity of applications. It also delves into the concept of restriction of applications, showing how to consider the application and its restriction. The lecture concludes with a detailed explanation of injectivity conditions and the combinatorial proof of the number of injections in the context of linear algebra.