This block consists of five lectures and one homework set (see homework page).

There are also office hours where you can ask questions about the homework and other things in the course.

Between lectures you should work on your own with the material shown in the asynchronous learning sections:

Video quizzes. These are mandatory.
Optional, but recommended, video material to watch for deeper understanding.
First homework set. Work on this during the whole block. The deadline is 5/2.

The reading material referenced is:

EJ0 = Background material on linear algebra, by Elias Jarlebring
EJ1 = Lecture notes on low-rank data algorithms, by Elias Jarlebring
PGM = Lecture notes on fast algorithms for big data, by Per-Gunnar Martinsson
GvL = Extract about SVD, from the book Matrix Computations, by Gene Golub and Charles van Loan

Recommended exercises are in the files:

AL19 = Active Learning 2019
AL20 = Active Learning 2020

OBS! The schedule below is preliminary. Minor changes may be made.

Date	Activities	Reading and recommended exercises
	Asynchronous learning 1 Quiz: Background linear algebra (optional) Video quiz 1: Low-rank approximation example	Reading: EJ0
14/1	Lecture 1 Course introduction Low rank approximations, general Slides Notes	Reading: EJ1: Sections 1-1.2.1 PGM: Sections 1.2, 1.3
	Asynchronous learning 2 Video quiz 2a: QR-factorization from Gram-Schmidt Video quiz 2b: Solving linear least squares via QR-factorization Homework 1	Reading: EJ1: Section 1.2
17/1	Lecture 2 QR-factorization variants/examples Reformulation of Gram-Schmidt CPQR - Low-rank approximation via partial QR Slides Notes	Reading: EJ1: Sections 1.2, 1.3 PGM: Section 1.5-1.5.3
	Asynchronous learning 3 Video quiz 3a: SVD introduction and properties Video quiz 3b: SVD and the Eckart-Young theorem Homework 1 Optional video material: An introduction to the singular value decomposition, by Steve Brunton The data matrix and SVD, by Steve Brunton SVD and the Netflix challenge, by Steve Brunton	Reading: EJ1: Section 1.4
21/1	Office hours
22/1	Lecture 3 Singular Value Decomposition (SVD) SVD by partial QR. Slides Notes	Reading: EJ1: Sections 1.3.4, 1.4, 1.5, 1.6 PGM: Section 1.4, 1.5.4, 1.5.5, GvL: Section 2.4.1, 2.4.3 + Theorem 2.4.8
	Asynchronous learning 4 Video quiz 4a: Index vectors Video quiz 4b: Randomized SVD, by PGM Homework 1 Optional video material: Watch more of the research talk on Randomized SVD, by PGM (Most important: time-point 01:59-19:50.) Enthusiastic talk about the worst data set ever, by Madeleine Udell	Reading: EJ1: Sections 1.6, 1.3.2
24/1	Lecture 4 Randomized SVD Slides Notes	Reading: EJ1: Section 1.6 PGM: Section 2.2-2.4.1, Theorem 2. Recommended exercises: AL20: 1-13, 1-41, 1-69, AL19: 1-13
	Asynchronous learning 5 Video quiz 5: Introduction to interpolatory decompositions Homework 1 Optional video material: Introduction to CUR A talk on ID in the context of multipole methods, by PGM. (The multipole method is used for solving e.g. elliptic PDEs. In the talk the matrix elements are a_ij=log(\|x_i -y_j\|), where physically x_i are the location of charges (sources) and y_j are points where the electric potential is sought (targets).)	Reading: EJ1: Section 1.7.1
28/1	Lecture 5 Interpolatory decomposition (ID) CUR Slides Notes	Reading: EJ1: Section 1.7 PGM: Section 4 (not 4.5.2, 4.6.2) Recommended exercises: AL20: 1-45, 1-55, 1-54, AL19: 1-16
5/2	Deadline Homework 1