Short description

Students are familiarised with and master the basic concepts and propositions of linear algebra and complex numbers. They can formulate simple concrete questions in the mathematical language and are able to solve these independently and present their solutions. 
Module coordinator

Landry Chantal (lany) 
Learning objectives (competencies)

Objectives 
Competences 
Taxonomy levels 
You know complex numbers in their different forms and can visualize them. 
F, M 
K2 
You can perform calculations with complex numbers. 
F, M 
K3 
You understand vectors as elements of a vector space. 
F, M 
K2 
You are familiar with the linear independence of vectors and can assess this using mathematical argumentation. 
F, M 
K2, K3 
You understand the concepts of linear span of a set of vectors and basis of a vector space. 
F. M 
K2 
You are able to determine a basis and the dimension of a vector space. 
F, M 
K3 
You understand the relationship between linear transformations and the matrix calculus, and know the transformation matrix of some geometric transformations. 
F, M 
K2, K3 
You understand the concepts of kernel and image of a linear transformation and are able to determine them. 
F, M 
K2, K3 
You can describe the change of basis between two bases of a vector space by a transformation matrix. 
F, M 
K2, K3 
You can compute the eigenvalues, eigenvectors and eigenspaces of a linear transformation. 
F, M 
K2, K3 

Module contents

Complex numbers:

The Cartesian complex plane

The different complex number forms

Operations with complex numbers

The fundamental theorem of algebra
Vector spaces:

The ndimensional vector space R^{n} and introduction to general vector spaces

Vector subspaces and subspace criterion

Linear independence of vectors

The linear span of a set of vectors, basis und dimension of a vector space
Linear transformations:

Linear transformations and matrices

Kernel, image and the ranknullity theorem

Applications: geometric transformations and change of basis
Eigenvalues and eigenvectors

Finding eigenvalues and eigenvectors

Multiplicity of eigenvalues

Applications: matrix diagonalization, constantcoefficient linear differential equations

Teaching materials

Lecture notes, blackboard sketches, handout 
Supplementary literature

Ruhrländer, M.: Lineare Algebra für Naturwissenschaftler und Ingenieure, Pearson Studium
Papula, L.: Mathematik für Ingenieure und Naturwissenschaftler (Bände I und II), Vieweg+Teubner, 12. Auflage
Gramlich, G.M.: Lineare Algebra: Eine Einführung, Carl Hanser Verlag

Prerequisites

Knowledge of mathematics of the technical Berufsmatura 
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 
Exams

Description 
Type 
Form 
Scope 
Grade 
Weighting 
Graded assignments during teaching semester 
at least 2 assessments 
written 
Per assessment max. 45 minutes 
Grade 
count only with a positive contribution to the final module grade with a total of 30%

Endofsemester exam 
Exam 
written 
90 min 
Grade 
Min 70% 

Remarks


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. 