Linear Systems: Factorization and Cholesky

This lecture covers the uniqueness of solutions in linear systems, the Cholesky factorization, LU factorization, and the cost of factorization. It also discusses the existence of solutions, regular matrices, and the formulation of linear systems. The instructor explains the importance of regular matrices, the factorization of Cholesky, and the cost of LU factorization. Additionally, the lecture delves into the cost of resolution, the main minors of matrices, and the precision of Hilbert matrices. The Sylvester criterion, iterative methods, and the resolution of systems using factorization are also explored.