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A course on computational linear algebra and applications. Topics include floating-point arithmetic algorithms and convergence Gaussian elimination for linear systems matrix decompositions (LU, Cholesky, QR) iterative methods for systems (Jacobi, Gauss Seidel) approximation of eigenvalues (power method, QR-algorithm) and also singular values and singular-value decomposition (SVD). Theoretical topics such as vector spaces, inner products norms, linear operators, matrix norms, eigenvalues and canonical forms of matrices (Jordan, Schur) are reviewed as needed. Matlab is used to solve all numerical exercises.