Syllabus:

# Matrix Computations and Applications, 7.5 Credits

Swedish name: Matrisberäkningar och tillämpningar

This syllabus is valid: 2021-07-26 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

Responsible department: Department of Computing Science

Revised by: Faculty Board of Science and Technology, 2021-06-15

## 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.

## Expected learning outcomes

Knowledge and understanding
After having completed the course the student will be able to:
• 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 (FSR 1)
Skills and Abilities
After having completed the course the student will be able to:
• use matrix computations in theory and practice to solve linear systems of equations and eigenvalue problems using modern software (FSR 2)
• apply matrix calculations within (a selection of) applications (FSR 3)
• apply a scientific approach to analyze and compile results with respect to the conditioning of the problem (FSR 4)
• report the results in writing (FSR 5)

## Required Knowledge

Univ: To be admitted you must have (or equivalent) 90 ECTS-credits including 60 ECTS-credits in Computing Science or two years of completed studies within a study programme (120 ECTS-credits). In both cases, the studies must include at least 15 ECTS-credits within Calculus, 7.5 ECTS-credits in Linear Algebra, at least 7.5 ECTS-credits within Programming methodology, and at least 4.5 ECTS-credits within Scientific computing/Numerical Analysis.

Proficiency in English equivalent to Swedish upper Secondary course English A/5. Where the language of instruction is Swedish, applicants must prove proficiency in Swedish 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

The examination consists of mandatory written assignments (FSR 2-5) and a mandatory written exam. The mandatory assignments are evaluated as approved or not approved.

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, all mandatory assignments must be approved. Then the grade is determined by the results on the written exam. The grade is done in the following way: When at least four of the five assignments are approved, the student is offered to take a written exam. The result of the exam is combined with the results of the mandatory assignments.

Deviations from the syllabus' modes of assessment can be made for a student who has a decision on pedagogical support due to a disability. Individual adaptation of modes of assessment must be considered based on the student's needs. The mode of assessment is adapted within the framework of the syllabus' expected learning outcomes. At the request of the student, the course coordinator, in consultation with the examiner, shall promptly decide on an adapted mode of assessment. The decision must then be notified to the student.

A student who, without receiving a passing grade, has participated in two tests for a course or part of a course, has the right to have another examiner appointed, unless special reasons militate against it (Högskoleförordningen 6 kap. 22 §). A request for a new examiner is made to the head of the Department of Computing Science.

During an academic year there are three opportunities for evaluation of the mandatory assignments and three opportunities to write the exam. A student who has passed an examination may not be re-examined.

If the student at the end of the academic year is approved for all five mandatory assignments, the grade 3 is obtained (regardless if a written examination is done or not). If the student has not passed the course after these occasions, all examination must be re-done at the next course offering.

A student who has taken two tests for a course or a segment of a course, without passing, has the right to have another examiner appointed, unless there exist special reasons (Higher Education Ordnance Chapter 6, Section 22). Requests for new examiners are made to the head of the Department of Computing Science.

Examination based on this syllabus is guaranteed for two years after the first registration of the course. This applies even if the course is closed down and this syllabus ceased to be valid.

TRANSFER OF CREDITS
Students have the right to be tried on prior education or equivalent knowledge and skills acquired in the profession can be credited for the same education at Umeå University. Application for credit transfer is submitted to the Student Services / Degree. For more information on credit transfer available at Umeå University's student web, see www.student.umu.se, and the Higher Education Ordinance (Chapter 6). A refusal of crediting can be appealed (Higher Education chapter 12) to the University Appeals Board. This applies to the whole as part of the application for credit transfer is rejected.

## Other regulations

This course may not be used towards a degree, in whole or in part, together with another course of similar content. If in doubt, consult the student counselors at the Department of Computing Science and / or the program director of your program.

In particular, this course can not, in whole or in part, be used in a degree together with 5DA002 Matrix Computations and Applications.

If the syllabus has expired or the course has been discontinued, a student who at some point registered for the course is guaranteed at least three examinations (including the regular examination) according to this syllabus for a maximum period of two years from the syllabus expiring or the course being discontinued.

## Literature

### Valid from: 2021 week 30

Strang Gilbert
Introduction to linear algebra
5th ed. : [Wellesley, MA] : Cambridge Press : 2016 : x, 574 s. :
ISBN: 978-0-9802327-7-6
Mandatory
Search Album, the University Library catalogue