Course Syllabus
Lecturer: Benjamin Schröter schrot@kth.se
Assistant: Anna Schenfisch schenf@kth.se
The schedule is available here. The topics and recommended exercise of each module can be found here.
Please also take a look at the general information provided on the same page. In particular, read the section about the course structure and study techniques as well as the section about the seminars. Further information on the intended learning outcomes and content of the course 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 on YouTube or the GeoGebra's 3D-Calculator to visualize concepts in two and three dimensional space.
You may find the lecture notes here:
- Lecture 1 - Vectors, norms, dot and scalar products and projects
- Lecture 2 - Projections, lines and planes
- Lecture 3 - Solving systems of linear equations I
- Lecture 4 - Solving systems of linear equations II
- Lecture 5 - Matricies
- Lecture 6 - More on matricies
- Lecture 7 - Vector spaces and linear (in)dependence
- Lecture 8 - Determinants
- Lecture 9 - The geometry of determinants
- Lecture 10 - Linear maps and transformations
- Lecture 11 - Orthogonal matrices and eigenvectors
- Lecture 12 - More on linear maps and an introduction to bases and dimension
- Lecture 13 - More on bases and fundamental spaces of matrices
- Lecture 14 - Orthonormal bases and the Gram-Schmidt method
- Lecture 15 - The method of least squares and basis/coordinate change
- Lecture 16 - Bases change and diagonalization
- Lecture 17 - More on bases changes, diagonalization and orthogonal diagonalization
- Lecture 18 - Quadratic forms (take a look at drawings of the level sets/curves) [interactive tools: Level Curves by Sarah Harrelson and Conic Sections by Tim Brzezinski]
- Lecture 19 - General vector spaces
- Lecture 20 - Discussion of exam questions I
- Lecture 21 - Discussion of exam questions II