Matrix Computations and Applications

Education facts

Code: 5DA003

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.

Entry requirements

At least 90 ECTS, including 60 ECTS Computing Science, or 120 ECTS within a study programme. At least 7.5 ECTS programming; 7.5 ECTS linear algebra; 15 ECTS differential and integral calculus; and 4.5 ECTS numerical analysis. Proficiency in English equivalent to the level required for basic eligibility for higher studies.

Education offerings

Each offering has its own dates and conditions. Closed offerings are retained as history and do not mean that a new application is open.

• Matrix Computations and Applications

  Umeå University

  Start date: 31 August 2026

  End date: 1 November 2026

  Pace of study: 50 %