Basic ideas and concepts in linear algebra: vectors, matrices, systems of linear equations, Gaussian elimination, matrix factorization, vector geometry with scalar product and vector product, determinants, vector spaces, linear independence, bases, change of basis, linear mappings, eigenvalue, eigenvector, the least squares methods, orthogonality, Gram-Schmidt's method.
Computational aspects: numerical solution of systems of linear equations with Gaussian elimination and LU factorization, complexity, determine complexity by numerical experiments, condition number and numerical computation of condition numbers, assessment of accuracy.
After the course the student should be able to
- use concepts. theorems and methods to solve and present solutions to problems within the parts of linear algebra described by the course content,
- use Matlab to solve problems within the parts of linear algebra and numerical analysis described by the course content,
- read and comprehend mathematical text.
in order to
- develop a good understanding for basic mathematical concepts within linear algebra and to use these for mathematical modeling of engineering and scientific problems,
- develop a skill, with the help of computers, to illustrate key concepts and solve applied problems with Matlab as well as to visualize and present the results in a clear way.
