Comments on Course or Lecture:

Syllabus:

Together with Analysis, Linear Algebra is considered to be one of the two basic fields of Mathematics. Linear Algebra methods are used in almost all advanced fields of mathematics, both theoretical and applied. In the second term we shall use the concepts, ideas and methods introduced in the first term. We shall study linear transformations and matrices, their eigenvalues and eigenvectors, their normal forms (diagonalization, Jordan normal form). We shall apply these methods to special kinds of matrices like orthogonal and unitary matrices, symmetric and hermetian matrices etc. We use these methods for the classification of quadratic surfaces. The concepts and methods developped in the course will be used in the second year in the course on Numerical Methods for solving numerically systems of linear equations and systems of ordinary linear differential equations. They are also applied in statistics, in computer graphics, and in other fields.

Prerequisites (necessary knowledge):

Linear Algebra I

Relevant Literature:

The contents of the course will be documented in a handout. Otherwise, the same books are recommended as in the first term.

Course Cycle:

every summer semester

Course Language:

English