Matrix Groups (MAT600)

An introduction to matrix groups and their applications.


Course description for study year 2024-2025

Facts

Course code

MAT600

Version

1

Credits (ECTS)

10

Semester tution start

Spring

Number of semesters

1

Exam semester

Spring

Language of instruction

English

Offered by
Time table

View course schedule

Content

NB! This is an elective course and may be cancelled if fewer than 10 students are enrolled by January 20th 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

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

Exam

Form of assessment Weight Duration Marks Aid
Oral exam 1/1 40 Minutes Letter grades None permitted

Individual assessment.

Course teacher(s)

Course coordinator:

Eirik Eik Svanes

Head of Department:

Bjørn Henrik Auestad

Method of work

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

Open for

Mathematics and Physics - Master of Science Degree Programme Mathematics and Physics - Five Year Integrated Master's Degree Programme

Course assessment

There must be an early dialogue between the course supervisor, the student union representative and the students. The purpose is feedback from the students for changes and adjustments in the course for the current semester.In addition, a digital subject evaluation must be carried out at least every three years. Its purpose is to gather the students experiences with the course.

Literature

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