ELEC60021 Mathematics for Signals and SystemsLecturer(s): Prof PierLuigi Dragotti Aims
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.
Learning Outcomes
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 leastsquare solution for overdetermined problems and minimum norm solution for underdetermined problem 5. find the Total Least Square solution to an approximation problem 6. compute the rank and the null space of a matrix Syllabus
Vector spaces (subspaces, linear independence and dimension, linear transformations); Inner product spaces (orthogonality, projections, GramSchmidt procedure); Computations with matrices and solution of system of equations (leastsquares, minimum norm solutions, pseudoinverse); Singular Value Decomposition; Total least squares problems.
Exam Duration: 3:00hrs Exam contribution: 100% Coursework contribution: 0% Term: Autumn Closed or Open Book (end of year exam): Closed Coursework Requirement: To be announced Oral Exam Required (as final assessment): N/A Prerequisite module(s): None required Course Homepage: https://bb.imperial.ac.uk Book List: Please see Module Reading list
