FEM3220 Matrix Algebra 10.0 credits
The course will be given in English.
The intention is that the course should be suitable as one of the first postgraduate courses in the PhD program. We will refresh and extend the basic knowledge in linear algebra from previous courses in the undergraduate program. Matrix algebra is of fundamental importance for scientists and engineers in many disciplines. In this course we will have a slight focus on topics that are of particular interest in Electrical Engineering.
The course requires a large amount of self-study and homework problems will be handed out every week and will be due the following week. It assumes some familiarity with basic concepts from linear algebra, as can be expected by good knowledge from undergraduate studies.
Information for research students about course offerings
Given in period 4 every even year.
Content and learning outcomes
Course contents
1. Review of vector spaces, inner product, determinants, rank
2. Eigenvalues, eigenvectors, characteristic polynomial
3. Unitary equivalence, QR-factorization
4. Canonical forms, Jordan form, polynomials and matrices
5. Hermitian and symmetric matrices, variational characterization of eigenvalues, simultaneous diagonalization
6. Norms for vectors and matrices
7. Location and perturbation of eigenvalues
8. Positive definite matrices. Singular value decomposition
9. Nonnegative matrices, positive matrices, stochastic matrices
10. Stable matrices; Lyapunovs theorem
11. Matrix equations and the Kronecker product, Hadamard product
12. Matrices and functions square roots, differentiation
Additional topics selected for the student presentations
Intended learning outcomes
After the course, each student is expected to:
· Show a good working knowledge of some fundamental tools (specified by the course content) in matrix algebra.
· Use the acquired knowledge to more easily apprehend research papers in engineering.
· Identify research problems in which matrix algebra tools may be powerful.
· Apply the knowledge to solve the identified matrix algebra problems.
· Combine several sub problems and solutions to solve more complex problems.
· Show improved skills in problem solving and proof writing as well as in critical assessment of proofs and solutions.
· Show improved skills in oral presentation of technical contents.
Course disposition
Literature and preparations
Specific prerequisites
Doctoral students at the School of Electrical Engineering. External participation by admission of the examiner.
Recommended prerequisites
Equipment
Literature
Examination and completion
If the course is discontinued, students may request to be examined during the following two academic years.
Grading scale
Examination
- EXA1 - Examination, 10.0 credits, grading scale: P, F
Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.
The examiner may apply another examination format when re-examining individual students.
Other requirements for final grade
● Individual solutions to weekly written homework assignments, 80% of max score (Written exam if homework not satisfactorily solved)
● Peer-review grading of assigned problem sets
● Presentation of assigned topic and actively participating during other students presentations
Opportunity to complete the requirements via supplementary examination
Opportunity to raise an approved grade via renewed examination
Examiner
Ethical approach
- All members of a group are responsible for the group's work.
- In any assessment, every student shall honestly disclose any help received and sources used.
- In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.
Further information
Course web
Further information about the course can be found on the Course web at the link below. Information on the Course web will later be moved to this site.
Course web FEM3220