Lecture notes
The schedule is available here. The topics and recommended exercise can be found here.
There is plenty of additional material, videos or interactive tools available. Examples, that I can recommend, are the linear algebra series by 3Blue1Brown Links to an external site. on YouTube or the GeoGebra's 3D-Calculator Links to an external site..
Here is a solution to part (a) of problem 3.2 from the exercise sheet of module 4:
Problem 3.2 Download Problem 3.2
You may find the lecture notes here:
- Lecture 1 Download Lecture 1 - Vectors, norms, dot and scalar products and projects
- Lecture 2 (there are no notes - this will be an exception)
- Lecture 3 Download Lecture 3 - Solving systems of linear equations I
- Lecture 4 Download Lecture 4 - Solving systems of linear equations II
- Lecture 5 Download Lecture 5 - Matricies
- Lecture 6 Download Lecture 6 - More on matricies
- Lecture 7 Download Lecture 7 - Determinants
- Lecture 8 Download Lecture 8 - The geometry of determinants
- Lecture 9 Download Lecture 9 - Vector spaces and linear (in)dependence
- Lecture 10 Download Lecture 10 - Linear maps and transformations
- Lecture 11 Download Lecture 11 - Orthogonal matrices and eigenvectors
- Lecture 12 Download Lecture 12 - More on linear maps and an introduction to bases and dimension
- Lecture 13 Download Lecture 13 - More on bases and fundamental spaces of matrices
- Lecture 14 Download Lecture 14 - Orthonormal bases and the Gram-Schmidt method
- Lecture 15 Download Lecture 15 - The method of least squares and basis/coordinate change
- Lecture 16 Download Lecture 16 - Bases change and diagonalization
- Lecture 17 Download Lecture 17 - More on bases changes, diagonalization and orthogonal diagonalization
- Lecture 18
Download Lecture 18 - Quadratic forms (take a look at drawings of the level sets/curves)
[interactive tools: Level Curves by Sarah Harrelson Links to an external site. and Conic Sections by Tim Brzezinski Links to an external site.] - Lecture 19 Download Lecture 19 - General vector spaces
- Lecture 20 Download Lecture 20 Discussion of exam questions (part B&C) of 2022-10-24 and 2021-10-25