MATS132 Linear Lie Groups (4 cr)
Study level:
Advanced studies
Grading scale:
0-5
Language:
Finnish
Responsible organisation:
Department of Mathematics and Statistics
Curriculum periods:
2017-2018, 2018-2019, 2019-2020
Description
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
Completion methods
Exercises and a course exam, or a final exam
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
- 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
Description of prerequisites
Linear algebra and geometry 1-2, Algebra 1 (groups), Multivariable calculus 1A and 1B (or Vector Calculus 1 and 2)
Literature
- Baker, Andrew. Matrix groups: An introduction to Lie group theory.
- Stillwell, John. Naive Lie theory.
- Tapp, Kristopher. Matrix groups for undergraduates.
Completion methods
Method 1
Select all marked parts
Parts of the completion methods
x
Teaching (4 cr)
Type:
Participation in teaching
Grading scale:
0-5
Language:
Finnish