Linear Algebra: Dot Product and Pre-Hilbertian Spaces

This lecture covers the concept of pre-Hilbertian spaces, focusing on the dot product and metric defined by equality. It discusses the properties of scalar product and norms in vector spaces, emphasizing the equivalence standards. The lecture also delves into the algebraic bases of vector spaces, exploring the implications of finite and infinite dimensions. Additionally, it presents examples of transformations and approximation theorems in the context of pre-Hilbertian spaces.