This website is no longer updated.

As of 1.10.2022, the Faculty of Physics has been merged into the TUM School of Natural Sciences with the website For more information read Conversion of Websites.

de | en

Mathematics for Physicists 1 (Linear Algebra)

Module MA9201

This Module is offered by Department of Mathematics.

This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.

Module version of SS 2012 (current)

There are historic module descriptions of this module. A module description is valid until replaced by a newer one.

Whether the module’s courses are offered during a specific semester is listed in the section Courses, Learning and Teaching Methods and Literature below.

available module versions
SS 2012WS 2011/2

Basic Information

MA9201 is a semester module in German language at Bachelor’s level which is offered in winter semester.

This Module is included in the following catalogues within the study programs in physics.

  • Fundamentals Examination (GOP, Part 1) in the B.Sc. Physics
Total workloadContact hoursCredits (ECTS)
240 h 90 h 8 CP

Content, Learning Outcome and Preconditions


Basic notions (sets and set operations, maps, families), vector spaces (linear subspaces, linear span, generating set, linear independence, basis, dimension), linear maps (kernel, range, dimension relation, solution space of a linear equation, isomorphism), matrices (matrices vs. maps, matrix calculus, change of basis), linear systems of equations (elimination method, solution space in parameter and basis representation), determinants, eigenvalues (eigenspaces, diagonalisability, characteristic polynomial, triangularisability), vector spaces with scalar product (Cauchy-Schwarz inequality, orthonormal basis, Gram-Schmidt orthogonalisation, orthogonal projection, best approximation), diagonalisation of normal endomorphisms, principal axis transformation

Learning Outcome

After successful completion of the module students are able to use the language of modern mathematics. They are able to analyse abstract relations, they can argue coherently and they are familiar with isomorphism classes. They are capable of recognising linear structures and represent them using matrices, for whose treatment they are equipped with matrix calculus.


Mathematical knowledge within the scope of the general qualification for university entrance

Courses, Learning and Teaching Methods and Literature

Courses and Schedule

Learning and Teaching Methods

lecture, exercise module, tutorials, assignments
The module is offered as lectures with accompanying practice sessions. In the lectures, the contents will be presented in a talk with demonstrative examples, as well as through discussion with the students. The lectures should motivate the students to carry out their own analysis of the themes presented and to independently study the relevant literature. Corresponding to each lecture, practice sessions will be offered, in which exercise sheets and solutions will be available. In this way, students can deepen their understanding of the methods and concepts taught in the lectures and independently check their progress. At the beginning of the module, the practice sessions will be offered under guidance, but during the term the sessions will become more independent, and intensify learning individually as well as in small groups.


problem sets, lectures notes


Meyberg K., Vachenauer, P.: Höhere Mathematik 1, Springer 1999.
Fischer G.: Lineare Algebra, Vieweg 2005.
Jänich, K.: Mathematik 1 (Geschrieben für Physiker), Springer 2005.
Lang, S.: Linear Algebra, Springer 1987.

Module Exam

Description of exams and course work

The module examination is based on a written exam (90 minutes). Students have to know linear structures and can represent them with matrices. They are able to deal with matrix calculus and to abstract and argue precisely under time pressure.

General Remarks on Exams within Fundamentals Examination (GOP, Part 1) in the B.Sc. Physics

The written exams in the mandatory modules of the first year in the Bachelor’s program Physics are subject to the rules of the Fundamentals Examination (GOP). Each non-passed exam may only be repeated once. If after the repeat exams of one semester the student failed in one and only one of the three exams a rescue exam is granted where the grade may be corrected to 4,0.

By act of the examination regulations (FPSO) students in the Bachelor’s program Physics are registered to the module exams. To support exam organisation egular registration via TUMonline is done anyway. For students that do not show up at the exam the exam is counted as failed.

Exam Repetition

The exam may be repeated at the end of the semester.

Current exam dates

Currently TUMonline lists the following exam dates. In addition to the general information above please refer to the current information given during the course.

Exam to Mathematics for Physicists 1 (Linear Algebra)
Prüfung ist Teil der Grundlagen- und Orientierungsprüfung im Bachelorstudiengang Physik. // Exam is part of the Fundamentals and Orientation Examination (GOP) in the B.Sc. Physics.
Top of page