Lecture: LU-decomposition

Seminar (Lab): Implementing LU-decomposition in code, solving SLEs with the help of it

Lecture: Transposes, permutations, symmetric matrices, and a link to LU-decomposition

Seminar: Solving problems on that

Lecture: Vector spaces, subspaces, the null-space of Ax=0

Seminar: Solving problems on that

Lecture: The rank and the row-reduced form

Seminar: Solving problems on that

Lecture: (Finally!) Completely solving Ax=b

Seminar: Solving problems on that
(+Gauss-Jordan elimination)

Lecture/Seminar: Linear independence, basis, dimension, span

Lecture/Seminar: The four subspaces for Ax=b – the row and column space, the null-spaces

Lecture: Orthogonal spaces, orthogonality of the four subspaces, projections onto subspaces

Seminar: Solving problems on that

Lecture: Projection matrices and the least squares approximation

Seminar (Lab): Numerous least squares approximation applications, (maybe) a bit on the Moore-Penrose pseudoinverse

Lecture: Orthogonal bases and the Gram-Schmidt procedure

Seminar: Solving problems on that, (maybe) a bit on special orthogonal bases

Lecture/Seminar: Determinants, permutations, cofactors

Lecture/Seminar: Cramer’s rule for matrix inverse, determinant as volume

Final exam

Lecture: Introduction. Vectors, linear combinations, the dot product, vector’s length

Seminar (Lab): Vectors in Python & NumPy, comparing data with the dot-product

Lecture: Systems of linear equations (SLEs)

Seminar: Solving problems on SLEs

Lecture: (Gaussian) Elimination: the idea of it, elimination in terms of (augmented) matrix notation for SLEs

Seminar: Solving SLEs with elimination. Commenting on the code implementation of GE

Lecture: Matrices and matrix operations, inverse matrices

Seminar: Solving problems on matrix arithmetic