t.BA.XXM3.LA2.19HS (Linear Algebra 2)
Module: Linear Algebra 2
This information was generated on: 16 June 2024
No.
t.BA.XXM3.LA2.19HS
Title
Linear Algebra 2
Organised by
T IAMP
Credits
4

### Description

Version: 4.0 start 01 February 2024

#### 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 n-dimensional vector space Rn 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 rank-nullity theorem

• Applications: geometric transformations and change of basis

Eigenvalues and eigenvectors

• Finding eigenvalues and eigenvectors

• Multiplicity of eigenvalues

• Applications: matrix diagonalization, constant-coefficient 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

( ) Yes (X) No

Type 2b

#### 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%` End-of-semester exam Exam written 90 min Grade Min 70%

#### 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.

### Note

Course: Lineare Algebra 2 - Vorlesung
No.
t.BA.XXM3.LA2.19HS.V
Title
Lineare Algebra 2 - Vorlesung

### Note

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