t.BA.XXM5.LA1.19HS (Linear Algebra 1) 
Module: Linear Algebra 1
This information was generated on: 30 July 2021
Linear Algebra 1
Organised by


Version: 2.0 start 01 February 2019

Short description

In this course, students learn the basic tools of linear algebra. These include vector and matrix calculus and the solution of linear equation systems. You also learn how to calculate with complex numbers and to use them in a number of applications.

Module coordinator

Schmid Matthias (scmi)

Learning objectives (competencies)

Objectives Competences Taxonomy levels

You know complex numbers and their arithmetic operations in their various representations and you are able to use them among other things for the description of alternating electrical currents.

F, M K2, K3

You are familiar with geometric calculus. You are
able to
compute norm, inner products, orthogonal
projection, and
cross product of vectors and use
vectors to describe geometric objects.

F, M K2, K3

You are able to recognize systems of linear equations and use suitable methods to solve them. In addition, you can apply the linear least square method to overdetermined systems of linear equations.

F, M K2, K3
You are familiar with the basic operations of matrix calculus.
These include the calculation of matrix products, determinants,
inverse matrices, etc
F, M K2, K3

Module contents

          Real Numbers and Introduction to Complex Numbers

  • Number sets: real numbers and field axioms

  • Complex numbers and the complex plane

  • Calculus with complex numbers (summation and multiplication)

  • Polar form of complex numbers (polar coordinates, modulus and argument)

    Geometric Calculus

  • Vectors in R^2 and R^3

  • Norm of a vector, inner product and angle between vectors

  • Orthogonal Projection

  • Parametric representations of lines and planes in R^3

  • Cross Product of vectors

    Matrix Calculus

  • Matrizen, Matrixprodukt

  • Solution of systems of linear equations, Gauss elimination and row echelon form

  • LU decomposition

  • Linear least squares

  • Inverse Matrix

  • Determinant

    Complex Numbers

  • Euler‘s formula and exponential form of complex numbers

  • Exponential and powers of complex numbers

  • Application of complex numbers to AC current.

  • Graphical representation of complex functions (Nyquist and Bode plots)

Teaching materials

Depending on the lecturer

Supplementary literature

  • Lernbuch Lineare Algebra und Analytische Geometrie,
    Gerd Fischer, Florian Quiring,

    Springer Spektrum Verlag, 2. Auflage,

  • Lineare Algebra für Naturwissenschaftler und Ingenieure,
    Michael Ruhrländer,
    Pearson Studium
    ISBN 978-3-86894-271-2

  • Formeln, Tafeln, Begriffe (Mathematik, Physik, Chemie),
    Orell Füssli Verlag,
    ISBN 978-3-280-04059-1


Knowledge of mathematics of the "technische Berufsmaturität"

Teaching language

(X) German ( ) English

Part of International Profile

( ) Yes (X) No

Module structure

Type 2b
  For more details please click on this link: T_CL_Modulauspraegungen_SM2025


Description Type Form Scope Grade Weighting
Graded assignments during teaching semester In consultation written or orally   Grade 20%
End-of-semester exam Exam written 120 min Grade 80%



Legal basis

The module description is part of the legal basis in addition to the general academic regulations. It is binding. During the first week of the semester a written and communicated supplement can specify the module description in more detail.
Course: Lineare Algebra 1 - Vorlesung
Lineare Algebra 1 - Vorlesung


  • No module description is available in the system for the cut-off date of 01 August 2099.