Quadratic Best Approximation

This lecture covers the concept of the best quadratic approximation in a finite-dimensional vector space with a scalar product, i.e., an Euclidean space. It explains how to find the closest vector in a subspace to a given vector, defining the best approximation as the one minimizing the squared distance. The proof involves applying the Pythagorean theorem to show the optimality of the projection. The lecture emphasizes the importance of this concept in the context of least squares approximation. The instructor illustrates the theory with mathematical propositions and remarks, providing a deep understanding of the topic.