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406-0173-AAL

Linear Algebra I and II

Belegung ist NUR erlaubt für MSc Studierende, die diese Lerneinheit als Auflagenfach verfügt haben. Alle anderen Studierenden (u.a. auch Mobilitätsstudierende, Doktorierende) können diese Lerneinheit NICHT belegen.
VVZ CR n/a

Last Updated: 2026-07-21 00:35:41

Abstract

Linear algebra is an indispensable tool of engineering mathematics. The course is an introduction to basic methods and fundamental concepts of linear algebra and its applications to engineering sciences.

Objective

After completion of this course, students are able to recognize linear structures and to apply adequate tools from linear algebra in order to solve corresponding problems from theory and applications. In addition, students have a basic knowledge of the software package Matlab.

Content

Systems of linear equations, Gaussian elimination, solution space, matrices, LR decomposition, determinants, structure of linear spaces, normed vector spaces, inner products, method of least squares, QR decomposition, introduction to MATLAB, applications. Linear maps, kernel and image, coordinates and matrices, coordinate transformations, norm of a matrix, orthogonal matrices, eigenvalues and eigenvectors, algebraic and geometric multiplicity, eigenbasis, diagonalizable matrices, symmetric matrices, orthonormal basis, condition number, linear differential equations, Jordan decomposition, singular value decomposition, examples in MATLAB, applications. Reading: Gilbert Strang "Introduction to linear algebra", Wellesley-Cambridge Press: Chapters 1-6, 7.1-7.3, 8.1, 8.2, 8.6 A Practical Introduction to MATLAB: http://www.math.ethz.ch/~grsam/Numerik_MAVT_WS0203/docs/intro.pdf Matlab Primer: http://www.math.ethz.ch/~grsam/Numerik_MAVT_WS0203/docs/primer.pdf

Resources

Literature

- Gilbert Strang: Introduction to linear algebra. Wellesley-Cambridge Press - A Practical Introduction to MATLAB: http://www.math.ethz.ch/~grsam/Numerik_MAVT_WS0203/docs/intro.pdf - Matlab Primer: http://www.math.ethz.ch/~grsam/Numerik_MAVT_WS0203/docs/primer.pdf - K. Nipp / D. Stoffer, Lineare Algebra, vdf Hochschulverlag, 5. Auflage 2002 - K. Meyberg / P. Vachenauer, Höhere Mathematik 1, Springer 2003

General Information