Linear Algebra, Honours Course, 6 credits

Main field of study

Course level

Advancement level

Course offered for

• Biomedical Engineering, M Sc in Engineering
• Applied Physics and Electrical Engineering, M Sc in Engineering
• Mathematics
• Computer Science and Engineering, M Sc in Engineering
• Industrial Engineering and Management - International, M Sc in Engineering
• Industrial Engineering and Management, M Sc in Engineering
• Information Technology, M Sc in Engineering
• Applied Physics and Electrical Engineering - International, M Sc in Engineering
• Computer Science and Software Engineering, M Sc in Engineering

Entry requirements

Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshold requirements for progression within the programme, or corresponding.

Prerequisites

Intended learning outcomes

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

Course content

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. 

Teaching and working methods

Lectures and assigned problems to be handed in.
The course runs over the entire spring semester.

Examination

Grades

Department

Director of Studies or equivalent

Examiner

Course website and other links

Education components

Course literature