Course

Matrix Groups (MAT600)

Facts

Course code MAT600

Credits (ECTS) 10

Semester tuition start Spring

Language of instruction English

Number of semesters 1

Exam semester Spring

Time table View course schedule

Literature Search for literature in Leganto

Introduction

An introduction to matrix groups and their applications.

Content

This course will not be taught in spring 2026 and 2027

NB! This is an elective course and may be cancelled if fewer than 10 students are enrolled by January 20 for the spring semester.

This course gives an introduction to matrix groups and their applications. Matrices as linear transformations of vector spaces over the real numbers, complex numbers and quaternions will be introduced. The associated general linear, special linear and orthogonal groups will be defined in each case, with lots of examples and applications to symmetry groups. The topology of a matrix group will be described. The structure of matrix groups as manifolds will also be covered, and the important notion of a Lie algebra associated with a matrix group will be developed.

Learning outcome

After completing the course, the student should have knowledge of how to use matrices to describe general linear, special linear and orthogonal groups over the real numbers, complex numbers and quaternions. They should also be familiar with the most common examples in low dimension. The student should also know how to think of matrix groups as topological spaces, and indeed as manifolds. Moreover, the student should also be able to derive the Lie algebra of a matrix group and compute its Lie bracket.

Required prerequisite knowledge

None

Recommended prerequisites

Mathematical Methods 1 (MAT100), Linear Algebra (MAT110), Discrete Mathematics (MAT120), Real Analysis (MAT210), Abstract Algebra (MAT250), Vector Analysis (MAT300), Differential Equations (MAT320), Manifolds (MAT510)

Exam

Oral exam

Weight 1/1

Duration 40 Minutes

Marks Letter grades

Aid None permitted

Individual assessment.

Method of work

4-6 hours of lectures and problem solving per week.

Open for

Mathematics and Physics - Master Mathematics and Physics - Master

Admission requirements

Must meet the admission requirements of one of the study programmes the course is open for.

Course assessment

The faculty decides whether early dialogue will be held in all courses or in selected groups of courses. The aim is to collect student feedback for improvements during the semester. In addition, a digital course evaluation must be conducted at least every three years to gather students’ experiences.

Contact

Head of Department:
Bjørn Henrik Auestad
Course coordinator:
Eirik Eik Svanes

Offered by

Faculty of Science and Technology

Department of Mathematics and Physics

The course description is retrieved from FS (Felles studentsystem). Version 1