Eigenvalues and Eigenvectors

This lecture covers the concept of eigenvalues and eigenvectors, explaining how they are used to analyze linear systems. The instructor discusses the properties of eigenvectors, the calculation of eigenvalues, and the application of these concepts in solving linear systems. Various methods, such as LU factorization and iterative methods like Jacobi and Gauss-Seidel, are presented for solving linear systems. The lecture also addresses the impact of rounding errors on the solutions of linear systems and the importance of preconditioning matrices in numerical computations.