Symbolic Linear Algebra

1 General Information

Lecture: Spezialvorlesung Symbolisches Rechnen: Symbolische Linear Algebra.
LVA-Nr.: 326.080 (2019S)
Lecturer: Dr. Johannes Middeke
Email: jmiddeke (AT) risc.jku.at

2 Summary

The lecture will focus on finding exact solutions of systems of linear equations. The topics include:

diophantine equations (ie, systems over Euclidean domains),
matrix normal forms,
applications of normal forms.

3 Time and Room

The lecture will be held on Thursdays, 16:15–18:00 and the room is (Science Park) S3 047.

4 Materials

We provide a script (PDF) for the lecture which contains the definitions, theorems, examples, and exercises and which will be frequently updated throughout the term.

The current version of the script is from June 24, 2019.

Here is an alternative version of the Euclidean algorithm (PDF) with a slightly shorter proof.

5 Format

The course is held as a lecture. All classes will be taught in English.

6 Prerequisites

Students are expected to have basic knowlegde in linear algebra. In particular, they should be familiar with fields, vector spaces, and matrices.

7 Grading

The grade in this course will be determined by a written exam which will take place on June 27, 16:25–17:55 (ie, during the last class of this term starting 10 minutes late).

The exam will not include Chapter 15 (The Popov Normal Form) of the script.

Here is the 2017 exam (PDF).