Linear Algebra HS23
Week 1: Vectors and linear combinations
- Recommended: Chapters 0-2 of 3b1b Essence of Linear Algebra (see Resources)
Week 2: Linear independence, dot product
- Recommended: Chapter 3 of 3b1b Essence of Linear Algebra (see Resources)
Week 3: Matrix multiplication, CR decomposition, Gaussian Elimination
- This book has a good and more in depth explanation of Gaussian Elimination
Week 4: solution set of SLE, inverse of a matrix and how to find it, LU decomposition
- My approach for solving the Moodle quiz “(In)dependent columns in 3 by 3 matrix” can be found here
Week 5: LU decomposition continued, vector spaces, subspaces, basis, dimension, column/null space
Week 6: Column and null space of a matrix, how to compute a basis for them, revision of concepts from previous weeks
Week 7: RREF, general solution of SLE, geometric interpretation of matrix vector multiplication, fundamental subspaces
Week 8: Solutions to recap exercise and quiz, tips on writing proofs
- This week we did a recap on the material covered in the first half of the course. The used material (exercises and quiz) can be found here.
Week 9: Fundamental subspaces, least squares, orthonormality
Week 10: Projections, orthonormality, Gram-Schmidt, Pseudoinverses
Week 11: Pseudoinverses, Determinant
Week 12: Determinant, Complex Numbers, Eigenvalues and eigenvectors
You can find the quiz here.
I collected a few short proof exercises here which I can recommend! Especially the statement of exercise 1 is quite interesting and important.
This pdf contains on complex numbers and might be helpful for solving exercises 3,4,7 (they’re quite extensive, the most important facts can be found in my).
This book has proofs on properties of the determinant if you’re interested.
Week 13: Change of basis, Eigenvalue decomposition, Spectral Theorem
- You can find this week’s quiz here and solutions in the.
Week 14: Singular Value Decomposition
You can find this week’s quiz here and solutions in the.
Resources
Course site (lecture schedule and): https://ti.inf.ethz.ch/ew/courses/LA23/index.html
Course Moodle (exercises): https://moodle-app2.let.ethz.ch/course/view.php?id=20361
I personally recommend to do as many of the exercises as possible - I believe one can learn the most this way!
Videos that explain topics of linear algebra and show geometric interpretations:
If you want to use linear algebra in code or test/compute stuff:
- https://numpy.org/ (Python)
- https://www.wolframalpha.com/ (easy text input)
Some textbooks that I personally like and can recommend! I personally think it’s a good idea to use multiple textbooks: It might be that one author’s way of explaining concepts works much better for you than that of others.