BITL1 - Introduction to Linear Algebra - Fall 2021

Other offerings of this course: Fall 2021, Spring 2022, Spring 2023

Time: Tuesdays 14:00 - 15:40, Fridays 9:00 - 10:40
Instructor: Jānis Lazovskis, janis.lazovskis@rbs.lv
Office: 404, Skolas iela 11
Office hours: Thursdays 16:00 - 17:00 in person, or bookable online: calendly.com/jlazovskis
Internal page: ORTUS e-studijas

Course material

Syllabus and calendar of the course
Lecture notes (updated weekly)
Midterm topics to be tested on Oct. 15
Textbook (Strang's "Introduction to Linear Algebra")

Homework assignments

Assignment 1: Due at the start of class Friday, September 10
Assignment 2: Due at the start of class Friday, September 24
Assignment 3: Due at the start of class Friday, October 8
Assignment 4: Due at the start of class Tuesday, November 2
Assignment 5: Due at 23:59 on Wednesday, November 17
Assignment 6: Due at the start of class Friday, December 3

Python and Mathematica code

Lecture 10: Inner products and distances
- pilsetas-dist.npy: a distance matrix of distances among cities
- pilsetas-vardi.npy: names of the cities to accompany the matrix above
- pilsetas.py: code to use both the above files and create a dendrogram
Lecture 16: Singular value decomposition
- Python notebook: for working with the singular value decomposition of a matrix
- Image repository: some small grayscale and color test images to decompose
Lecture 17: Principal component analysis
- Python notebook: for working with PCA of data sets
- pca-augstskolas: data set in CSV or Python pandas PKL of university instuctors and students in 2020 (source: Oficiālais Statistikas Portāls)
- pca-decathlon: data set in CSV or Python pandas PKL of 2004 decathlon results (source: Prof Dhafer Malouche)
Lecture 19: Jordan form
- Python notebook: for computing generalized eigenvectors
Lecture 21: Fourier topics
- Python notebook: for computing and plotting Fourier approximations in sine and cosine basis
- discrete-fourier-transform.nb: Mathematica notebook for computing and plotting Fourier approximations in the exponential basis
Lecture 24: Graph clustering
- Python notebook: for creating, weighting, and plotting graphs

Exams

Midterm: covering lectures 1-12
Solutions to midterm
Final exam: covering lectures 13-25. Released Monday, December 6. Due Monday, December 20, 23:59.
Solutions to final exam