| TATA53 |
Linear Algebra, Honours Course, 6 ECTS credits.
/Linjär algebra, överkurs/
For:
D
I
Ii
IT
Mat
U
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 maps
- use the singular value decomposition in applications
- use the theory of positive matrices in applications
- 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. Norms and scalar products. Direct sum. Matrix factorizations: LU, Cholesky, QR. Schur factorization. The spectral theorem for Hermitian and normal maps. The singular value decomposition with applications. Low-rank approximation, pseudoinverse, least square problems, polar factorization. The Cayley-Hamilton theorem. Invariant subspaces. Generalized eigenvectors. The Jordan normal form. Applications to systems of differential and difference equations. Positive matrices. The Perron and Frobenius theorems. Applications to ranking models. Introduction to multilinear algebra. Dual spaces, tensors, tensor product, Kronecker product.
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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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