Linear Algebra: Orthogonal Projections

This lecture covers the concept of orthogonal projections in linear algebra, focusing on the projection of vectors onto subspaces. It explains the process of obtaining orthogonal families and bases, as well as the properties of orthogonal and orthonormal bases. The lecture also discusses the projection of vectors onto subspaces, the best quadratic approximation of a vector in a subspace, and solving systems of equations using least squares solutions. The instructor emphasizes the importance of understanding orthogonal projections in various applications.