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Syllabus:

# Matrix Computations and Applications, 7.5 Credits

Swedish name: Matrisberäkningar och tillämpningar

This syllabus is valid: 2024-06-24 and until further notice

Course code: 5DA003

Credit points: 7.5

Education level: Second cycle

Main Field of Study and progress level: Computing Science: Second cycle, has only first-cycle course/s as entry requirements
Computational Science and Engineering: Second cycle, has only first-cycle course/s as entry requirements

Grading scale: TH teknisk betygsskala

Responsible department: Department of Computing Science

Revised by: Faculty Board of Science and Technology, 2024-04-04

## Contents

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.

## Expected learning outcomes

Knowledge and understanding
After completing the course, the student should be able to:

• (FSR 1) account for basic concepts such as the four fundamental subspaces, projections, transformations (homogeneous and inhomogeneous), orthogonality and angles, rank, matrix factorizations (eg LU, QR and SVD), conditioning and stable algorithms.

Competence and skills
After completing the course, the student should be able to:

• (FSR 2) use matrix computations in theory and practice to solve linear systems of equations and eigenvalue problems using modern software,
• (FSR 3) apply matrix calculations within (a selection of) applications,
• (FSR 4) apply a scientific approach to analyze and compile results with respect to the conditioning of the problem,
• (FSR 5) report the results in writing.

## Required Knowledge

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.

## Form of instruction

Education consists primarily of lectures and classroom exercises. In addition to scheduled activities, individual work with the course material and in computer labs are required.

## Examination modes

Part 1, theory (FSR 1 - 4), is assessed by a written exam in halls. The grade scale on this part is Fail (U), Pass (3), Pass with Merit (4), or Pass with Distinction (5).

Part 2, practice (FSR 2 - 5), is assessed by written assignments. The grade scale on this part is Fail (U) or Pass (G).

On the course as a whole, one of the grades Fail (U), Pass (3), Pass with Merit (4), or Pass with Distinction (5) are given. To pass, both modules must be passed. Then the grade is determined by the grade on part 1.