Linear Algebra

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, determinants
- the student is familiar with the general theory of finite-dimensional vector spaces, in particular with the concepts of basis and dimension
- the student 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 problem
- diagonalization of symmetric matrices
- quadratic forms
- singular value decomposition

FORM OF TUITION
2 lectures and 1 exercise class per week

TYPE OF ASSESSMENT
Six bi-weekly tests (20 percent, only the best five 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 the following two numbers: 0.2 times the average of the best five tests plus 0.8 times the result of the resit and just the resit.