Linear Algebra I
The following is a concrete example of Linear Algebra, recently given in
Bielefeld. In general the contents vary slightly from year to year.
For the content of the current course in Linear Algebra I and II, please also
take a look at the course homepage and the
German homepage of the course.
- Basic
Set theory. Semigroup and group. Rings and fields
- Matrix (with coefficients from a commutative ring)
Addition and multiplication. Mutiplication of scalars. Elementry row and column operations. Determinant. Characteristic polynomail of a matrix
(Cayley-Hamilton Theorem)
- Vector space and linear transformation
Basis of a vector space, and linearly independent set. Dimension of
subvector space. Linear maps and matrices. Dimension of the kernel and
cokernel of a linear maps
- Endomorphisms
Eigenvalue and Eigenvector. Eigenvalue as a root of the chracterstic polynomail. Triangulation of matrices and linear maps. Nilpotent matrices
Literature
- Fischer, Lieaner Algebra
- Fischer, Analytische Geometrie
- Lang, Linear Algebra, Springer Verlag
- Artin, Algebra, Birhaeuser Verlag
- Fuhrmann A polynomial approach to linear algebra, Springer Verlag