Welcome to the Matrix Theory course home page. The goal of the course is to discuss matrices at a level more advanced than in basic courses, focusing also on the interactions of matrix theory with abstract algebra on one hand and numerical analysis on the other hand.
In 2020/21 this course will be taught fully online. Everything will be organized remotely, including lectures, exercise sessions, and exams.
More information on the software will appear nearer the time.
Exercises: Friday 12:15 to 14 (from 6.11 to 4.12)
Written Exam (optional, see below): Friday 11.12 12:15 to 14
Project Presentations (optional, see below): To be agreed on an individual basis.
- Matrices over general commutative rings.
- Matrices over principal ideal domains: Hermite and Smith canonical forms.
- Matrices and pencils over fields. Canonical forms.
- Matrices over the ring of analytic functions. Rellich decomposition.
- Polynomial matrices. Linearizations. Numerical methods for the polynomial eigenvalue problem.
- Theory and computation of matrix functions.
- Non-negative matrices. Perron-Frobenius theory.
Passing the course
There are two possibilities to pass the exam, either by solving a written exam or by presenting a project on some topic related to the course; suggestion on possible topics will be given during the course. With the first option, the grade will be 100% based on the exam, while with the second option the grade will be based 40% on the homework and 60% on the project.