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 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

Additional Information Teaching Methods

2 lectures and 1 exercise class per week

Method 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.

Literature

David C. Lay, Stephen R. Lay and Judi J. McDonald, Linear Algebra and
its Applications, 5th edition, Pearson Global Edition, ISBN-13
9781292092232

Additional Information Target Audience

1BA