# Symbolic Linear Algebra

## 1 General Information

- Lecture
- Spezialvorlesung Symbolisches Rechnen: Symbolische Linear Algebra.
- LVA-Nr.
- 326.080 (2019S)
- Lecturer
- Dr. Johannes Middeke
- 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).