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Linear Algebra

Winter Term 2016/17

Practical exercise (short: UE for german "Uebung") for the lecture Linear Algebra (PHY.C10) at the Technical University Graz. Details concerning the lecture or the UE can be found at the TUG-Online and at the description site by Priv.-Doz. Brauchart.

The exercises starts at October 20th and takes place either at the Physics Institute (Petersgasse 18), the Institute of Applied Mathematics of the Technical University Graz (Steyrergasse 30) or the Physcis Institute at the Karl-Franzens University Graz (Universitätsplatz 5). There are 3 Groups at each University due to the large amount of participating students (*: My Group):

Gruppe 1(*):

12:30 - 14:15 TDK-Seminarraum (PHEG016)

Gruppe 2:

15:00 - 16:45 HS AE01 (STEG112)

Gruppe 3:

16:45 - 18:30 HS AE01 (STEG112)

Gruppe Hilger:

13:15 - 15:00 HS 05.12 (0005010248)

Gruppe Knebl:

15:00 - 17:00 HS 06.02 (0006EG0022)

Gruppe Schmidt:

12:30 - 14:15 SR 05.13 - IGAM (0005010040)

Course Content

The lecture follows closely the lecture notes from Prof. Ganster in the winter term 2014/15. The course topics are (list may be incomplete):

  • Algebraic structures: Groups, Rings and Vectorspaces
  • Linear functions: Mappings and basis transformations
  • Matrix Calculations: Addition, Multiplication and other matrix operations
  • Solving systems of linear equations
  • Eigenvalues and Eigenvectors of matrices

Exercise Mode

In each exercise the problems from the exercise sheets (see "Supplemental Material") will be discussed. Therefore a random student who checked the problem in the Onlinesystem will be picked to present his solution at the blackboard.

The solved problems have to be checked online (at the "Online-Kreuzerlsystem") until 11:30 at the day of the exercise.
It is also possible to have 2 "Ersatzabgaben" if one can not participate at the exercise class (no excuse needed). Please send your solution to me via mail before the first group starts (i.e. 12:15 on that day) and check the problems in the Online system as "Ersatzabgabe". For all other exercises attendance is mandatory.


There will be two exams, one before Christmas and one at the end of the semester, for the exercise class and one for the lecture. The exams for the exercise and the one for the lecture are completely independent from another. For all the exams no books, lecture notes, smartphones or other electronic devices are allowed.

Exam dates:

Please make sure that you are enrolled for the exam in the TUG-Online system. Further exam dates for the lecture can be found in the TUG-Online.


For a positive grade there are two necessary requirements.

  • checked more than 50% of the problems on the exercise sheets
  • 40 points together at both exams (40 points each are possibles)

When this requirements are met, the grade will be put together by the following points.

  • Percentage of checked problems multiplied by 20 points
  • Sum of points on both exams

This leads to a maximum of 100 points. For a positive grade one needs at least 50 points. Further there is the possibility to get up to 5 extra points for active participation or very good presentations.

Supplemental Material

Here you can find the exercise sheets. It will be weekly updated.

  1. Exercise 0 (due: Oct 20 2016)
  2. Exercise 0.5 (due: Oct 27 2016)
  3. Exercise 1 (due: Nov 03 2016)
  4. Exercise 2 (due: Nov 10 2016)
  5. Exercise 3 (due: Nov 17 2016)
  6. Exercise 4 (due: Nov 24 2016)
  7. Exercise 5 (due: Dec 01 2016)
  8. Exercise 6 (due: Jan 12 2017)
  9. Exercise 7 (due: Jan 19 2017)
  10. Exercise 8 (due: Jan 26 2017)
  11. Exercise 9 (due: Feb 02 2017)


The following list contains literature used in the lecture and some additional books and lecture notes favored by the siteowner.

  • K. Jänich: "Lineare Algebra"
  • G. Fischer: "Lineare Algebra, Eine Einführung für Studienanfänger"
  • C. Lang, N. Pucker: "Mathematische Methoden in der Physik", Second Edition (2005)
    (This book is a very good companion for the whole study of physics since it covers all topics neccessary for physicists)
  • M. Ganster: "Lecture Notes from WS 2014/15"; Link

Bernd Riederer

BSc MSc Bernd Riederer Institut für Physik

Mozartgasse 14/II
Room 0025-02-0004
8010 Graz

Phone:+43 316 380 - 5089

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