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Linear Algebra
Lineare Algebra
Last Updated: 2026-06-03 00:07:41
Abstract
Contents: Linear systems - the Gaussian algorithm, matrices - LU decomposition, determinants, vector spaces, least squares - QR decomposition, linear maps, eigenvalue problem, normal forms - singular value decomposition; numerical aspects.
Objective
You can: + solve linear systems of equations with the Gauss elimination; + interpret and appropriately use the standard operations with vectors and matrices; + compute and properly apply various matrix decompositions; + compute eigenvalues, eigenvectors and the determinant of a matrix; + use the properties of vector spaces and linear operators; + formulate and solve linear least squares problems with the appropriate methods; + understand and apply the singular value decomposition.
Content
+ linear systems of equations, matrices, Gauss-Elimination, LU and QR decomposition + linear spaces,first part of the fundamental theorem of linear algebra, choice of basis and change of coordinates + linear operators and change of variables + norm and scalar product in a linear space, Gram-Schmidt orthogonalisation, projectors + linear least squares problems + determinants + eigenvalues, eigenvectors, symmetric matrices + sigular value decomposition, second part of the fundamental theorem of linear algebra, applications
Resources
Lecture Notes
Vasile Gradinaru, Lineare Algebra, Vorlesungsskript an der ETH (seit 2014)
Literature
Vasile Gradinaru, Lineare Algebra, Vorlesungsskript an der ETH K. Nipp / D. Stoffer, Lineare Algebra, vdf Hochschulverlag, 5. Auflage 2002 P. J. Olver und C. Shakiban “Applied Linear Algebra”, 2nd ed. (2018) Gilbert Strang “Introduction to Linear Algebra”, 4th edition (2009)
General Information
- Language
- German
- Levels
- BSC , MSC
- Frequency
- Yearly recurring
Examination
- Type
- session examination
- Mode
- written 120 minutes
- Aids
- keine
- Digital
- The exam takes place on devices provided by ETH Zurich.
Course Components
| Type | Title | Time & Place | Hours |
|---|---|---|---|
| lecture |
Lineare Algebra
Am Freitag Vorlesung in HG F 1 mit Videoübertragung in HG F 3
|
No time listed | 3 h weekly |
| exercise |
Lineare Algebra
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Übungen in den einzelnen Übungsgruppen beginnen in der ersten Semesterwoche.
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|
No time listed | 2 h weekly |