MATS132 Linear Lie Groups (4 cr)
Grading scale
0-5
Teaching languages
Finnish
Responsible person(s)
Tero Kilpeläinen,
Learning outcomes
After completing the course, the student
- knows examples of matrix groups and their applications
- knows the definitions and basic properties of matrix exponential and matrix logarithm
- understands the connection between a matrix group and its Lie algebra
- knows how to determine the Lie algebra of a matrix group
Study methods
Exercises and a course exam, or a final exam
Content
-Real and complex matrix groups; orthogonal, affine and unitary groups
- rotations and quaternions
- matrix exponential and logarithm
- one parameter subgroups
- Lie algebra of a matrix group
Literature:
| ISBN-number | Author, year of publication, title, publisher |
|---|---|
| Baker, Andrew. Matrix groups: An introduction to Lie group theory. | |
| Stillwell, John. Naive Lie theory. | |
| Tapp, Kristopher. Matrix groups for undergraduates. |
Prerequisites
Linear algebra and geometry 1-2, Algebra 1 (groups), Multivariable calculus 1A and 1B (or Vector Calculus 1 and 2)