Linear Applications: Definitions and Examples

This lecture introduces linear applications, defining them as transformations from R^n to R^m that map each vector to a unique one. It covers properties of linear transformations, such as the superposition principle and consequences of the definition. Examples illustrate linearity and non-linearity, emphasizing the transformation of vectors and multiples. The lecture also explores implications and counterexamples related to the linearity of transformations, highlighting the importance of verifying linearity through specific cases.