*Conducted in term:*2022L

*Erasmus code:*11.1

*ISCED code:*0541

*ECTS credits:*5

*Language:*Polish

*Organized by:*Faculty of Physics

*Related to study programmes:*

# Algebra II E 1100-1Ind06

In the course we will continue to present important concepts of linear algebra. With some background material introduced in the course "Algebra I" we will focus more on analysis of linear operators, functional calculus and elements of analytic geometry. Towards the end of the semester we will deal with basics of abstract algebra.

**Program:**

1. Multilinear algebra and determinants - continued

(quadratic forms, diagonalization, bilinear forms on real vector spaces, signature, positivity, symplectic spaces)

2. Spectrum of an operator

(spectrum of an operator, eigenvectors, diagonalizable operators, Jordan basis, Jordana form)

3. Functional calculus

(the space of linear maps, functions of an operator)

4. Unitary spaces

(scalar products, unitary spaces, orthogonal projections, self adjoint and unitary maps, the spectral theorem in finite dimensional spaces)

5. Additional topics

(groups - permutations, roots of unity, linear groups, rings, algebras, modules, representations, affine spaces, affine maps)

There will be written and oral exams. To take the oral exam the student needs to score at least 50% of points in the written part. In order to take the written part 50% of points from mid-term tests must be scored.

June 2007, Piotr Sołtan

## Course coordinators

## Bibliography

1. P. Urbański "Algebra dla studentów fizyki" (skrypt WF UW)

2. A. Białynicki-Birula "Algebra"

3. A. Mostowski, M. Stark "Algebra liniowa"

## 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:

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