Linear Algebra, 7.5 credits, FOR058F
Educational level: third-cycle course.
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. M0049M or equivalent course. Basic knowledge of MATLAB-programming.
Course content: Basic concepts: vector spaces, subspaces, linear independence, basis and dimension, matrices, inner product spaces. Duality: linear functionals, annihilator, quotient spaces, codimension, tensors. Spectral theory: eigenvalues, Cayley-Hamilton theorem, generalized eigenvectors, Jordan normal form, Perron-Frobenius theorem, stochastic matrices, QR decomposition, polar decomposition, singular value decomposition (SVD). 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 as well as deduce similar relationships.
- 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, 2025
Course is given periodically:
Send application to: John Fabricius, john.fabricius@ltu.se
Deadline for application: October 15
Course open for application by doctoral students admitted to other universities than LTU: No
Limited number of students: 20
Tuition:
Contact person: John Fabricius, john.fabricius@ltu.se, 0920-492594
Examiner: Peter Wall
Updated: