Orthogonal Bases and Projection

This lecture covers the concept of orthogonal bases, the projection onto subspaces, and the Gram-Schmidt process for constructing an orthogonal basis. It explains how to find the closest vector in a subspace and the properties of orthogonal matrices. The lecture also introduces the Gram-Schmidt algorithm and its application in creating orthogonal bases. The instructor demonstrates the process step by step, emphasizing the importance of orthogonality in linear algebra.