Direct Methods for Solving Linear Equations

This lecture covers direct methods for solving systems of linear equations, focusing on the factorization of non-singular matrices into lower and upper triangular matrices, and permutation matrices. It also discusses the memory usage and the factorization of full, band, and sparse matrices, including their LU factorizations. The lecture explores the impact of round-off errors on the solutions of linear systems and the condition number of matrices. Additionally, it delves into the effects of perturbations on exact systems and the properties of symmetric and positive definite matrices.