Projection in Vector Spaces

This lecture covers the generalization of projection in vector spaces, specifically focusing on the projection of a vector onto a subspace. It explains the unique properties of the projection, its geometric interpretation, and the best approximation of a vector in a subspace. The lecture also introduces the concept of orthogonal bases and how they relate to projections. The theorems presented emphasize the significance of projections in vector spaces and their role in finding the closest vector in a subspace to a given vector.