Gram-Schmidt Algorithm: Orthogonalization and QR Factorization

This lecture covers the Gram-Schmidt algorithm for orthogonalizing a basis of a vector space, leading to the construction of an orthonormal basis. It also discusses the QR factorization method, aiming to factorize a matrix into an orthogonal matrix and an upper triangular matrix. The lecture further explores the method of least squares, focusing on finding the best-fitting solution for an incompatible system of linear equations. Various theorems related to these topics are presented, emphasizing the importance of linear independence and the uniqueness of solutions. Practical examples are provided to illustrate the theoretical concepts.