# MM562: Advanced Linear Algebra

## Comment

## Entry requirements

## Academic preconditions

## Course introduction

In relation to the competence profile of the degree it is the explicit focus of the course to:

Knowledge: Give the students knowledge on concepts, constructions and theorems in linear algebra (dimension, tensor products, spectral theory, linear transformations).

Skills: Give the students the skills to solve concrete problems in linear algebra (find the dimension of a vector space, describe linear transformations with respect to different bases, find eigenvalues and eigenvectors for normal operators). Give the students the skills to work with different operations on vector spaces and to analyse the properties of concrete linear transformations.

Competences: Give the students the competences to 1) Discuss and collaborate with others around mathematical problems within the field of linear algebra, concerning solution methods and theory, while applying standard mathematical terminology. 2) Switch fluently between abstract theory and concrete mathematical examples and understand the interaction between abstract theory and concrete problems.

## Expected learning outcome

The learning objective of the course is that the student demonstrates the ability to:

- Apply mathematical theory and results and methods to solve concrete problems in advanced linear algebra.
- Argue in a mathematically correct way concerning the steps and techniques applied in the solution of given problems within advanced linear algebra.
- Assess whether achieved results are correct.
- Present mathematical arguments in written form.
- Master minor proofs within the curriculum

## Content

The following main topics are contained in the course:

- operations on vector spaces (dual spaces, tensor products, direct sums, quotient spaces, determinants)
- spectral theory for normal operators
- linear transformations and their properties

## Literature

## Examination regulations

## Exam element a)

## Timing

## Tests

## Written exam

## EKA

## Assessment

## Grading

## Identification

## Language

## Examination aids

To be announced during the course

## ECTS value

## Additional information

## Indicative number of lessons

## Teaching Method

At the faculty of science, teaching is organized after the three-phase model ie. intro, training and study phase.

The lectures, where the literature (curriculum) for the course will be explained, will be supplemented by exercise classes, where relevant exercises, relating to the lectures, will be solved and explained. Both of these events are supported by the students' independent work (or group-work) on the material as described in the study phase.

- Read the literature for the course
- Solve exercises