Matrix Groups (MAT600)
An introduction to matrix groups and their applications.
Course description for study year 2023-2024. Please note that changes may occur.
Facts
Course code
MAT600
Version
1
Credits (ECTS)
10
Semester tution start
Spring
Number of semesters
1
Exam semester
Spring
Language of instruction
English
Time table
Content
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 |
Course teacher(s)
Course coordinator:
Martin Gunnar GulbrandsenHead of Department:
Bjørn Henrik AuestadMethod of work
4 hours of lectures and problem solving per week.
Open for
Course assessment
There must be an early dialogue between the course coordinator, the student 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 course evaluation must be carried out at least every three years. Its purpose is to gather the students experiences with the course.