*This course is not currently conducted!*

*Erasmus code:*11.1

*ISCED code:*0541

*ECTS credits:*unknown

*Language:*Polish

*Organized by:*Faculty of Physics

# Algebra with Geometry 1100-1INZ14

1. Basic algebraic structures. Real and complex numbers.

2. Systems of linear equations, matrices, Gauss elimination.

3. Operations on matrices.

4. Matrices as an example of algebra, inverse of a matrix.

5. Permutation group, determinants.

6. Properties of determinatns. Kramer's formulae, Laplace expansion.

7. Minors, ranges of matrices, inverting matrices.

8. Vector spaces - linear independence, bases.

9. Linear transformations and connection with matrices.

10. Eigenvalues and eigenvectors. Hamilton-Cayley theorem. Functions of matrices.

11. Change of basis, invariants of endomorphisms.

12. Linerar spaces with product. Gram-Schmidt orthogonalization.

13. Unitary and hermitian operators.

14. Quadratic forms, classification of quadrics.

Expected amount of student's labour: 130 hours including 60 hours of lectures and tutorials, 45 hours of homework and 25 hours for preparations to the examinations and the exam itself.

## Type of course

## Mode

## Prerequisites (description)

## Learning outcomes

The student should be able to use vectors, linear transformations, matrices. He/she should know the notion and applications of dot product, determinants, eigenvalues, eigenvectors and eigenspaces of linear transformations, rank-2 manifolds in n-dimensional spaces.

## Assessment criteria

In order to pass the course, the student will have to pass recitations (based on two colloquia and short class tests) and the final exam. The details will be announced at the beginning of the semester after consultations with instructors.

## Bibliography

1. A. Białynicki-Birula, Algebra liniowa z geometrią

2. J. Klukowski, I.Nabiałek Algebra dla studentów Wydawnictwa Naukowo Techniczne , 2004

3. Jacek Komorowski, Od liczb zespolonych do tensorów, spinorów, algebr Liego i kwadryk.

4. J.A. Mostowski i M. Stark, Algebra liniowa

5. S. Gancarzewicz, Algebra liniowa z elementami geometrii, Wydawnicwo Naukowe UJ, Kraków, 2001.

## Additional information

Information on *level* of this course, *year of study* and semester when the course
unit is delivered, types and amount of *class hours* - can be found in course structure
diagrams of apropriate study programmes. This course is related to
the following study programmes:

- Nuclear Power Engineering and Nuclear Chemistry, full time 3 year programme leading to B. Sc. Degree
- Nanostructure Engineering, first cycle programme

Additional information (*registration* calendar, class conductors,
*localization and schedules* of classes), might be available in the USOSweb system: