Numerical linear algebra

• Absolute and relative error, Condition number of a problem, floating point arithmetic, rounding error, stability of algorithms, computational complexity.
• Solving linear systems: preliminar notions, triangular systems, gaussian elimination, pivotal strategies, LU and Choleski factorizations.
• QR factorization of square nonsingular matrices.
• QR factorization of full-rank non-square matrices and rank-deficient matrices, QR factorization with column pivoting. Numerical rank.
• SVD decomposition, Moore-Penrose pseudoinverse, Moore-Penrose conditions.
• Computing the SVD decomposition.
• Conjugate gradient.