Linear Algebra
Website for my exercise sessions for the course Linear Algebra at ETH Zurich. This website is not officially affiliated with ETH Zürich.
This website does not guarantee correctness. First trust the official lecture material, then your intuition and never anything on this website.
The material below heavily quotes publicly available lecture material for the course 401-0131-00L offered in ETH Zurich written by B. Gärtner, A.S. Bandeira and R. Weismantel.
Weekly notes
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Week 0
Vectors and Linear Combinations
Vectors, vector addition and scalar multiplication, linear combinations, row and column pictures, and affine, conic and convex combinations.
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Week 1
Lengths, Angles and Linear Independence
The scalar product, the Euclidean norm, Cauchy–Schwarz, angles, orthogonality and hyperplanes, the triangle inequality, linear independence and span.
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Week 2
Matrices and Matrix Transformations
Matrices, matrix addition and scalar multiplication, matrix shapes, matrix–vector multiplication, column space, rank, the transpose, row space, the nullspace and matrices as matrix transformations.
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Week 3
Linear Transformations and Matrix Multiplication
Linear transformations and linear functionals, the matrix of a linear transformation, composition of linear transformations and matrix multiplication, ways to multiply matrices, image and kernel.
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Week 4
CR Decomposition and Inverse Matrices
The CR decomposition, bijective functions, why only square matrices can be invertible, invertible and singular matrices, the inverse and its properties.
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Week 5
Linear Systems of Equations and Gauss Elimination
Linear systems of equations Ax = b, Gauss elimination with back substitution, elimination and permutation matrices, invariance under invertible row operations, runtime, and computing the inverse.
Contact
- mkilic @ ethz.ch
- Where
- CHN C 14
- When
- Thursdays 8.15 - 10.00