QR Factorization and Least Squares

This lecture covers the factorization QR, where a matrix A can be decomposed into the product of an orthonormal matrix Q and an upper triangular matrix R. The process involves finding an orthonormal basis of the column space of A, ensuring the diagonal elements of R are positive. Additionally, the lecture introduces the least squares method, which aims to find the vector closest to the column space of A when a system of equations has no exact solution. Through examples and the Gram-Schmidt process, the instructor demonstrates how to compute the QR factorization and apply the least squares method to solve such systems.