## Linear Algebra

course no.
401-0131-00
semester
Fall 2022
lecturers
Özlem Imamoglu,
Olga Sorkine-Hornung
coordination
Jing Ren,
Alexandre Binninger,
Danielle Luterbacher
lecture
Wed 10-12; HG F 7, HG F 5 (stream)
Fri 10-12; HG F 7, HG F 5 (stream)
Live Stream
EduApp
Link to course channel on EduApp
video recording
ETH Videoportal
exercise
Thu 08-10/16-18, Fri 14-16
ECTS
7 credits

### news

19.12.2022
There will be no lecture on Friday, 23.12.2022.
22.09.2022
The EduApp link has been added to the webpage. You are encouraged to ask questions over there during lectures.
01.09.2022
Website online.

### content

Systems of linear equations, vectors and matrices, norms and scalar products, LU decomposition, vector spaces and linear maps, linear least squares problems, QR decomposition, determinants, eigenvalues and eigenvectors, singular value decomposition, applications.

### schedule and course notes

Date Notes Chapter in script

21.09.22
23.09.22
Introduction,
Complex numbers
0.3-0.4

28.09.22
30.09.22
Systems of linear equations (SLE),
Gauss algorithm
1.1-1.3

05.10.22
07.10.22
Matrices and vectors 2.1-2.3, 2.6

12.10.22
14.10.22
Inverse, orthogonal and unitary matrices,
LU decomposition
2.7-2.9,
3.1-3.2

19.10.22
21.10.22
Vector space, vector subspace, bases 4.1-4.3

26.10.22
28.10.22
Dimension, change of basis,
linear maps
4.3-4.4, 5.1

02.11.22
04.11.22
Kernel, image, matrix representation,
solution set of an SLE
5.1-5.5

09.11.22
11.11.22
Solution set of an SLE
Norm, scalar product, Cauchy-Schwarz inequality
6.1-6.2

16.11.22
18.11.22
Cauchy-Schwarz inequality, orthonormal bases
Parseval's identity, Gram-Schmidt process
2.4, 6.2-6.3

23.11.22
25.11.22
Orthogonal complements, fundamental subspaces, orthogonal/unitary matrices and maps, linear least squares 6.4-6.6,
7.1-7.2

30.11.22
02.12.22
Least squares, QR decomposition,
determinants
7.1-7.3,
8.1-8.3

07.12.22
09.12.22
Determinants, eigenvalues 8.1-8.3, 9.1

14.12.22
16.12.22
Eigenvalues, eigenvectors, spectral decomposition, spectral theorem, singular value decomposition 9.1-9.3, 11.1

21.12.22
23.12.22
Singular value decomposition.
No class.
11.1

### script

The relevant content for the exam is completely covered during the lecture. The following script is only provided for additional support.

### Matlab tutorials

Matlab exercises are not relevant for the exam. They are provided for completeness.
Content Starting Code
Introduction to Matlab
Learning Matlab by doing Matlab
Exercise 1 : Fibonacci fibonacci.m
Exercise 2 : Gauss Method gauss.m
Exercise 3 : Matrix Power
Exercise 4 : LU Decomposition
Exercise 5 : Pivot LU Decomposition
Exercise 6 : Interpolation
Exercise 7 : Gram Schmidt Algorithm
Exercise 8 : Curve Fittings ls_smooth.zip

### bonus assignments

During the semester, you can hand in solutions to the exercises clearly marked as bonus to acquire bonus points. The 10 best weeks will be taken into account. The acquired bonus points can increase the grade of the written exam by at most 0.25.

assignment submission to submit, you have to hand in a single PDF file via Moodle before the strict deadline listed below (no extension policy). You can convert and combine pictures of handwritten notes into a single PDF, or type the homework using LaTeX. Below we provide a ready-to-use LaTeX template. To use it, (1) sign up for overleaf using your ETH account; (2) drag the zip file below to start a new project; (3) compile the main.tex file.

• Assignment LaTeX template
• Inappropriate behavior when working on the assignments, such as copying the solutions of fellow students or other sources, or providing your own solution for others to copy, has serious consequences, including the dispossession of all the bonus points.

### exercises

Date (exercise session) Assignment Solution Hand in deadline
29.09.22/30.09.22 Assignment 1 Solution 1 07.10.22, 16:00
06.10.22/07.10.22 Assignment 2 Solution 2 14.10.22, 16:00
13.10.22/14.10.22 Assignment 3 Solution 3 21.10.22, 16:00
20.10.22/21.10.22 Assignment 4 Solution 4 28.10.22, 16:00
27.10.22/28.10.22 Assignment 5 Solution 5 04.11.22, 16:00
03.11.22/04.11.22

Assignment 6
Clarification: Change of Basis
Solution 6

11.11.22, 16:00

10.11.22/11.11.22 Assignment 7 Solution 7 18.11.22, 16:00
17.11.22/18.11.22 Assignment 8 Solution 8 25.11.22, 16:00
24.11.22/25.11.22 Assignment 9 Solution 9 02.12.22, 16:00
01.12.22/02.12.22 Assignment 10 Solution 10 09.12.22, 16:00
08.12.22/09.12.22 Assignment 11 Solution 11 16.12.22, 16:00
15.12.22/16.12.22 Assignment 12 Solution 12 23.12.22, 16:00
22.12.22/23.12.22 Assignment 13 Solution 13 No hand-in

### exercise groups

Zoom Links (restricted access. Use VPN outside of the ETH network. Instructions can be found here.)
assistant time place comment
Dong Ho Kang Thu 08-10 Online (see Zoom links above)
Petar Stamenkovic Thu 08-10 CAB G 57
Marko Mihajlovics Thu 08-10 CHN D 42
Silvan Weder Thu 08-10 IFW A 32.1 German
Elia Trachsel Thu 08-10 CHN D 46
Petr Hruby Thu 08-10 CHN C 14
Jana Dinger Thu 08-10 ML F 34
Aurel Gruber Thu 08-10 ML J 37.1
Muyang Du Thu 08-10 RZ F 21
Sergey Prokudin Thu 16-18 CHN D 44
Zichen Gui Thu 16-18 CHN D 42
Leander Diaz-Bone Thu 16-18 IFW A 34 German
Boyang Sun Thu 16-18 ETZ H 91
Floor Verhoeven Thu 16-18 Online (see Zoom links above)
Kaifeng Zhao Fri 14-16 ETZ E 7
Chen Guo Fri 14-16 Online (see Zoom links above)
Ziqi Wang Fri 14-16 CHN G 46
Tianxin Tang Fri 14-16 IFW C 31
Marcel Geppert Fri 14-16 IFW D 42 German
Aviv Segall Fri 14-16 LFW C 11
Elif Bilge Emanet Thu 08-10 CAB G 56

### exam

Written exam, 180 minutes. Aid: 6 one-sided A4 pages or 3 double-sided A4 pages of written notes (notes typed in LaTeX or similar and printed are allowed; they should be readable without a magnifying glass); a dictionary (English-German or other foreign language) as a paper book is allowed (no e-book or similar); no calculator.

previous exams (German)