FEM3220 Matrix Algebra 10.0 credits

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

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. 

Doctoral students at the School of Electrical Engineering. External participation by admission of the examiner.

If the course is discontinued, students may request to be examined during the following two academic years.

• 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.

●     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

Magnus Jansson

• 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.