Matrix Computations and Applications

The course provides knowledge and understanding of matrix computations in various applications. For this, deeper knowledge of theory, methods, algorithms and software is required for different classes of numerical linear algebra problems. Among other things, the course discusses projections, fundamental subspaces, transformations, orthogonality and angles, rank, matrix factors (eg LU, QR, SVD), condition numbers (ill-posed or well-posed problems), direct and iterative methods to solve linear systems of equations (e.g. Gauss-Seidel, SOR, Krylov subspace methods, pre-conditioning) and eigenvalue problems (canonical forms, methods for calculating all and/or a few number of eigenvalues ​​and associated eigenvectors). Furthermore, the course deals with how this knowledge and skills are used in a number of applications within, e.g., information retrieval on the internet, computer graphics, simulation, signal processing and engineering applications. Practice and in-depth understanding are acquired through computer labs. The course is split into two parts: **Part 1, theory, 4.5 ECTS** This part introduces theory, methods, and algorithms. **Part 2, practice, 3.0 ECTS** In this part, numerical software is developed and used to solve problems in practical applications.