| TATA53 |
Linear Algebra, Honours Course, 6 ECTS credits.
/Linjär algebra, överkurs/
For:
D
I
Ii
IT
Mat
Y
Yi
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Prel. scheduled
hours: 38
Rec. self-study hours: 122
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Area of Education: Science
Main field of studies: Mathematics, Applied Mathematics
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Advancement level
(G1, G2, A): G2
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Aim:
This course extends the first course in linear algebra so that the student will be prepared for advanced courses in mathematics and applied subjects. After completing the course the student will be able to
- describe basic concepts and properties of complex vector spaces
- use and prove the spectral theorem for Hermitian and normal operators
- calculate the singular value decomposition and apply it to least squares problems
- determine and apply the Jordan canonical form
- use linear algebra in solving systems of differential and difference equations
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Prerequisites: (valid for students admitted to programmes within which the course is offered)
A basic course in linear algebra.
Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshhold requirements for progression within the programme, or corresponding.
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Organisation:
Lectures and assigned problems to be handed in.
The course runs over the entire spring semester.
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Course contents:
Complex vector spaces, with and without scalar product. Direct sum. Dual spaces. The spectral theorem for Hermitian and normal operators. Tensor products. Singular value decomposition. Cayley-Hamilton theorem. Invariant subspaces. Jordan normal form. Applications to systems of differential and difference equations. Positive matrices with applications.
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Course literature:
Treil, S: Linear Algebra Done Wrong
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Examination: |
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Hand-in exercises
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6 ECTS
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Course language is Swedish/English.
Department offering the course: MAI.
Director of Studies: Jesper Thorén
Examiner: Göran Bergqvist
Link to the course homepage at the department
Course Syllabus in Swedish
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