Thomas Keilen Linear Algebra II - ST 2004
Research Interests
Curriculum Vitae


Lecture: We 11:45-13:15, Rm 52-206 (Gert-Martin Greuel)
Fr 10:00-11:30, Rm 46-110 (Gert-Martin Greuel)
Example Class: Th 08:00-09:30, Rm 48-582 (Marc Dohm)
Th 10:00-11:30, Rm 11-260 (Kai Dehmann)
Th 10:00-11:30, Rm 32-439 (Hannah Markwig)
Fr 11:45-13:15, Rm 48-538 (Nadine Cremer)
Support Class: Mo 15:30-17:00, Rm 36-265 (Thomas Keilen)
Mo 17:15-18:45, Rm 46-260 (Thomas Keilen)


  1. Ergebnisse der Nachklausur in Linearer Algebra II: Ergebnisse, Statistiken zur Klausur.
    Mindestpunktzahlen: 14 Punkte = 4, 23 Punkte = 3, 32 Punkte = 2, 40 Punkte = 1.
  2. Einige Eindrücke von der Wanderung der Linearen Algebra II (von Kai und Thomas) sowie vom Treffen der LA-I-Übungsgruppe bei Hannah.
  3. Ergebnisse der Klausur in Linearer Algebra II: Statistiken zur Klausur.
    Mindestpunktzahlen: 15 Punkte = 4, 20 Punkte = 3, 25 Punkte = 2, 32 Punkte = 1.
    Beachtet bitte, daß einige Teilnehmer aufgrund der Übungen auf eine bessere Notenstufe gehoben wurden!
  4. Informationen zur Klausur in Linearer Algebra II
  5. Am Freitag, den 23. Juli, wandert die Lineare Algebra! Treffpunkt ist (voraussichtlich) 13:00 Uhr auf dem Parkplatz hinter dem Mathegebäude. Es ist geplant, anschließend auf dem Grillplatz hinter Gebäude 48 zu grillen.
  6. The destribution into example and support classes for linear algebra II can now be viewed here.
  7. The Singular exercises will this time be marked by the tutors of the example classes. In order to hand in a Singular exercise for marking, please print out the procedure and hand it in to the tutors pigeon hole. Then send your complete library to the tutor by email. Please mark clearly on the print out in case the procedure does not yet work!


Post Script Files: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 .
PDF-Files: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 .
Singular Prozeduren: determinante , param , zeilenvielfaches , zeilentausch , sgauss .


Most of the literature available in the library is in German, and most of the English literature on linear algebra concentrates on the theory of vector spaces, excluding most of the contents of the first part of this course. For this you will rather have to look at books on algebra.
J. Hefferon, Linear Algebra, Lecture Notes (2001)
P. Cohn, Algebra Vol. I, Wiley (1974)
W. Greub, Linear Algebra, Springer Verlag (1975)
S. Lang, Algebra, Springer Verlag (2002)
G. Fischer, Lineare Algebra, Vieweg Verlag (1998)
K. Jaenich, Linear Algebra, Springer Verlag (1981)
W. Klingenberg, Lineare Algebra und Geometrie, Springer Verlag (1990)
M. Koecher, Lineare Algebra und analytische Geometrie, Springer Verlag (1983)
E. Brieskorn, Lineare Algebra und analytische Geometrie I, Vieweg Verlag (1983)
H.-D. Ebbinghaus, et al., Zahlen, Springer Verlag

The lecture notes Mathematik für Informatiker, 1992/93, by Professor Greuel offer a short compendium of the contents of the lecture, however, omitting all proofs. They are available for purchase from the secretary Mrs. Kranz in room 48-527.

A more complete set of notes, Lineare Algebra II, 2000, which also includes most of the contents of the lecture, including the proofs, can be viewed in the library.

General Information:

Throughout the lecture the essential contents of linear algebra will be presented in a systematical way.

Once a week you will receive a set of exercises. These serve as a means to practise the methods of proof shown in the lecture and to recapitulate and understand its contents. The participants of the example classes are encouraged to work together with their fellow students in order to solve the exercises, and they may hand in their solutions in groups of two students. The solutions will then be marked and discussed throughout the example class meetings.

The support class in linear algebra is a meeting designed purely to answer questions which could not be clarified in the lecture or the example class. The participants are supposed to bring their questions, and we hope to be able to give answers in return - where possible, answers based on examples. Nevertheless, you should not miss any opportunity to ask questions also throughout the lecture and the example classes.

Every participant of the the lecture Linear Algebra I should register for one of the example classes and for one of the support classes by Wednesday, 28th April. This can be done using the web interface available at

Exam Regulations for the Lecture:

The regulations for the "Vordiplom", the "Zwischenprüfung" respectively the bachelor degree require a certain amount of credits which are obtained by participating successfully in example classes. In order to receive these credits for the lecture Linear Algebra II in the summer term 2004, you have to participate regularly in the example classes satisfying the following additional criteria:

  1. regular participation in the example classes (this includes that the exercises have been worked on in a sensible, not necessarily correct way), and
  2. the written exam in Linear Algebra II has to be passed.

The credit transcripts for the example class will be so called qualified transcripts, which means that they carry the mark obtained in the exam. However, should this result be considerably worse than your performance in the example classes, then your mark may be raised by one level. In particular, it is possible that you receive the credits even though you failed the exam! This, however, requires that the solutions which you handed in are clearly your own work and not just copied from somebody else. ("Own work" in this respect does not mean that you found them without cooperating with others, but that you wrote down the solution in your own understanding and your own words, and that you are capable of presenting them to your fellow students.)

Examination Date:

Exam in Linear Algebra II, Saturday, 17th July 2004, 09:00-12:00

Link to Information on Singular

Univ. of TübingenDept. of MathematicsSection AlgebraCAS SINGULAR