Matrix Groups (MAT600)

Content

This course will not be taught in spring 2026.

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

Recommended prerequisites

Exam

Course teacher(s)

Course coordinator:

Head of Department:

Method of work

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

Open for

Course assessment

Literature