Linear Algebra (4+5)

COURSE OBJECTIVE
After successfully completing this course, the student
- Has a working knowledge of the concepts of matrix algebra and finite-dimensional linear algebra, such as echelon form, LU decomposition, linear independence and determinants;
- Is familiar with the general theory of finite-dimensional vector spaces, in particular with the concepts of basis and dimension;
- Is familiar with the concepts of eigenvalues and eigenvectors, diagonalization and singular value decomposition and can apply these concepts in basic applications in discrete time dynamical systems;
- Has working knowledge of the concepts of inner product spaces and matrices acting in inner product spaces, including orthogonal
projections and diagonalization of symmetric matrices.

COURSE CONTENT
- Systems of linear equations
- Linear (in)dependence
- Linear transformations and matrices
- Matrix operations
- Determinants
- Vector spaces and subspaces
- Basis and dimension
- Rank of a matrix, dimension theorem
- Coordinate systems and change of basis
- Eigenvalues and eigenvectors
- Diagonalization of matrices
- Inner product, length and orthogonality
- Orthogonal bases and least-squares problems
- Diagonalization of symmetric matrices
- Singular value decomposition

TEACHING METHODS
2 lectures and 1 exercise class per week

TYPE OF ASSESSMENT
Four small tests (20 percent, only the best three are taken into account), a midterm exam (40 percent) and a final exam (40 percent).
There is a resit. For students taking the resit the final grade is determined by the maximum of 0.2 times the average of the best three tests plus 0.8 times the result of the resit and just the resit.