This course is an introduction to numerical Linear Algebra. Topics include: matrix  factorizations: QR-factorization, Cholesky factorization , vector and matrix norms: properties of the ‖.‖1,  ‖.‖2||  and ‖.‖   norms of vectors  in Rn,  properties of the ‖.‖1,  ‖.‖2|| , ‖.‖  and  ‖.‖F  norms of an mxn matrix, condition number of a  matrix, ill-conditioned systems, the Hilbert matrix,  perturbation analysis of linear systems, singular value decomposition (SVD) of an mxn matrix,  Moore-Penrose inverse, rank  k approximation of  a matrix, applications of the SVD to least-squares problems, iterative  methods for large sparse linear systems: the Jacobi and Gauss-Seidel methods,  the SOR method, applications to the solution of linear systems with banded coefficient matrices,  regularization methods for ill-conditioned linear systems, regularization of orders 0, 1 and 2, and the L-curve method for choosing an optimal regularization parameter.