The aim of this module is to present you with 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.

Upon successful completion of this module, you will be able to:
1. compute the trace, determinant, eigenvalues and eigenvectors of a matrix
2. compute the SVD of a matrix
3. critically analyse a linear mapping using the properties of the SVD
4. identify and find the least-square solution for overdetermined problems and minimum norm solution for under-determined problem
5. find the Total Least Square solution to an approximation problem
6. compute the rank and the null space of a matrix

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.