Linear Algebra

• Profs: Bernd Gärtner, Robert Weismantel
• Website: https://ti.inf.ethz.ch/ew/courses/LA24/index.html
• Moodle: https://moodle-app2.let.ethz.ch/course/view.php?id=23276
• Admin: Admin
• Material: Material
• Videos: Videos ETHZ
• Cheatsheet: cheatsheet.pdf

This linear algebra course, taught by Professors Gärtner and Weismantel, covered fundamental topics such as vectors, matrices and their operations, and solving linear systems, before progressing to concepts like orthogonality, projections, linear regression, eigendecomposition, and singular value decomposition.

While the course closely followed Professor Gilbert Strang’s MIT linear algebra course (which I highly recommend watching on YouTube), it delved deeper into mathematical proofs and rigor. It also included practical applications through “CS Lens,” which added an interesting perspective.

Overall, the course was well-structured, and its alignment with Strang’s material was helpful. However, I found that it sometimes focused too much on formal proofs rather than fostering an intuitive and visual understanding. That said, it’s still an excellent and educational course, especially given the wealth of online resources available on the topic.

Lecture Notes

• 01 Vectors
• 02 Vectors
• 03 Linear Dependence and Independence
• 04 Matrices and Linear Combinations
• 05 Transpose and Multiplication
• 06 CR-Factorization and Linear Transformations
• 07 Linear Transformations, Linear Systems of Equations, PageRank
• 08 Gauss Elimination, Elimination Matrices and Solution Sets
• 09 Elementary Row Operations, Gauss Elimination, Inverse Matrices, Inverse Theorem
• 10 Calculating the Inverse, LU and LUP Decomposition
• 11 Gauss-Jordan, REF, RREF, Properties of REF
• 12 Vector Spaces, Subspaces
• 13 Vector Spaces, Bases, Dimension
• 14 Fundamental Subspaces, Column Space, Row Space, Nullspace
• 15 Orthogonal Vectors and Orthogonal Complements of Subspaces
• 16 Orthogonal Complementary Subspaces, Projections, Normal Form
• 17 Projections, Least Squares, Linear Regression
• 18 Orthonormal Bases, Properties of Orthogonal Matrices
• 19 Gram-Schmidt Process, QR-Decomposition, Properties of Q and R
• 20 Pseudoinverses, Constructing Pseudoinverses
• 21 Certificates, Linear Systems of Inequalities, Projections of Polyhedra, Farkas Lemma
• 22 Determinants, Permutations, Properties, Cofactors, Cramers Rule
• 23 Eigenvalues and Eigenvectors, Complex Numbers
• 24 Explicit Fibonacci Formula, Eigenvalue and Eigenvector properties, Trace
• 25 Eigenvalues, Eigenvectors, Complete Set of Eigenvectors, Diagonalization, Eigendecomposition
• 26 Symmetric Matrices, Spectral Theorem, Rayleigh Quotient
• 27 Positive (Semi)Definite Matrices, Gram Matrices, SVD
• 28 SVD Theorem and Proof, SVD Abstraction, Pseudoinverse

Other Stuff

• Useful Resources