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Matrix Groups (MAT600)

An introduction to matrix groups and their applications.


Course description for study year 2022-2023. 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

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: Paul Francis de Medeiros
Head of Department: Bjørn Henrik Auestad
Method of work
4 hours of lectures and problem solving per week.
Open for
City and Regional Planning, Master of Science Computer Science, Master of Science Degree Programme Environmental Engineering, Master of Science Degree Programme Industrial economics, Master of Science Degree Programme Robot Technology and Signal Processing - Master's Degree Programme Structural and Mechanical Engineering, Master of Science Degree Programme Mathematics and Physics, Master of Science Degree Programme Mathematics and Physics, Five Year Integrated Master's Degree Programme Offshore Field Development Technology, Master of Science Degree Programme Industrial Asset Management - Master's Degree Programme Marine and Offshore Technology, Master of Science Degree Programme Offshore Technology - Master's Degree Programme Petroleum Geosciences Engineering, Master of Science Degree Programme Petroleum Engineering, Master of Science Degree Programme Technical Societal Safety, Master of Science Degree Programme Risk Management, Master's Degree Programme (Master i teknologi/siviling.)
Course assessment
Use of evaluation forms and/or conversation for students' evaluation of the course and teaching, according to current guidelines.
Literature
Search for literature in Leganto