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

This ETH Zürich Linear Algebra course, taught by Profs. Gärtner and Weismantel, introduces core concepts essential for computer science. Topics include vectors, matrices, linear transformations, systems of equations (e.g., Gaussian elimination, LU decomposition), fundamental subspaces, orthogonality, projections, least squares, the Gram-Schmidt process, and determinants. Emphasizing applications in graphics, machine learning, and data science, it builds a strong foundation for advanced studies and explores further topics beyond the basics.

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