Linjär algebra, 7,5 HP, FOR058F

COURSE SYLLABUS, third-cycle courses

Course name: Linear algebra

ECTS/HP: 7,5

Course code: FOR058F

Educational level: third-cycle course.

Eligibility requirements: The course is open for students admitted to third-cycle studies at LTU.

Entry requirements: Completed basic course in Linear algebra, e.g. M0067M or equivalent course. Basic knowledge of Matlab, Python or similar programming languages.

Course content: finite dimensional vector spaces, inner product spaces, linear maps, duality, tensors, spectral theory, Cayley-Hamilton theorem, generalized eigenvectors, Jordan normal form, self-adjoint maps, unitary maps, normal maps, matrix exponential, SO(3), Perron-Frobenius theorem, stochastic matrices, singular value decomposition (SVD), polar decomposition, steepest descent, iterative methods. Applications: principal component analysis (PCA), dimensionality reduction, Markov chains, differential equations, multilinear subspace learning.

Learning outcomes: After completing the course the student should be able to

• Explain how different theorems and concepts are connected within the area of mathematics described by the course contents.
• Use basic concepts and theorems within the parts of linear algebra as described by the course content to solve applied problems.

Course methods: Lectures and problem seminars.

Examination form: Written individual assignments, active participation in problem seminars.

Grading scale: Pass/Fail.

Course literature: Peter Lax, Linear Algebra and Its Applications, 2nd edition, John Wiley & Sons, New Jersey, 2007.

Education cycle: Sp 3-4, 2027

Course is given periodically:

Send application to: Peter Wall, peter.wall@ltu.se

Deadline for application: October 15 2026

Course open for application by doctoral students admitted to other universities than LTU: Yes

Limited number of students: 25

Tuition: No fee for PhD students enrolled at LTU

Contact person: Peter Wall, peter.wall@ltu.se, 0920-492018

Examiner: Peter Wall

Course syllabus decided by: Lars-Göran Westerberg, Head of PhD studies at TVM

Date of decision: 2026-02-18