The aim of this course is to present a comprehensive introduction to advanced topics in Linear Algebra as needed in the more advanced literature on Signals, Signal Processing, Systems and Control. The emphasis is on fundamental notions related to vector spaces, inner product spaces, normed spaces, matrix algebras and computations with matrices.

The students should gain familiarity with some mathematical concepts and methods that are routinely used in physics, engineering, probability and statistics, and economics: linear transformations, approximations, matrix decompositions, eigenvalues and eigenvectors, matrix computations.

Vector spaces (subspaces, linear independence and dimension, linear transformations); Inner product spaces (orthogonality, projections, Gram-Schmidt procedure); Computations with matrices and solution of system of equations (least-squares, minimum norm solutions, pseudoinverse); Singular Value Decomposition; Total least squares problems