Course Objectives

To develop an overview over problems that can be formulated as matrix equations, to acquire practice in formulating equations in matrix form, to analyze over determined, under determined and degenerate sets of equations, and to get an understanding of some methods to solve such equations.

Course Description

Brief repetition: Linear equations, row equivalence, rank, Gauss elimination, Echelon form, LU-decomposition. Vector spaces, linear mappings, basis, coordinates and coordinate changes. Orthogonality, inner products, QR-decomposition. Least squares method. Determinants. Eigenvalues, similar matrices, diagonalization. (Jordan canonical form). Functions of matrices, Cayley-Hamilton's theorem. Solution of linear differential equations, stability. Orthogonal projections. The spectral theorem for normal matrices. Quadratic forms. Main axis theorem. Sylvester theorem. Singular value decomposition.

Learning Methods

Lectures, colloquium, or self study w/ regular meetings with course responsible -- depending on the number of students and their background. Exercises and one intermediate test (project?), as well as the use of relevant software for PC.

Assessment Methods

The intermediate test counts 30%, and the final test counts 70% in the course grade.

No study aids are permitted at the final test.

Minor adjustments may occur during the academic year, subject to the decision of the Dean