Course syllabus

# Matristeori

Matrix Theory

## FMA120, 6 credits, A (Second Cycle)

## General Information

## Aim

## Learning outcomes

## Contents

## Examination details

## Admission

## Reading list

## Contact and other information

Matrix Theory

Valid for: 2014/15

Decided by: Education Board B

Date of Decision: 2014-04-08

Main field: Technology.

Compulsory for: Pi3

Elective for: BME4, C4-ssr, D4-bg, D4-ssr, E4-bg, E4-ra, F4, F4-tf, F4-bs, F4-bg, F4-r, F4-ss

Language of instruction: The course will be given in English on demand

The main aim of the course is to convey knowledge about concepts and methods from matrix theory and linear algebra which are important in applications within many subjects in technology, science and economy, , and familiarity with their use. In addition, the course should develop the student's ability in general to assimilate and communicate mathematical theory and to solve problems. Furthermore, the course should strengthen the student's ability in mathematical programming.

Knowledge and understanding

For a passing grade the student must

- independently be able to characterize and use different types of matrix factorizations.
- be able to understand and independently explain the theory of matrix functions, in particular polynomials, and its connection to the Jordan normal form.
- be able to describe different types of vector and matrix norms, and to compute or estimate them as well with as without computer support.
- be familiar with the common classes of normal matrices and their properties.

Competences and skills

For a passing grade the student must

- with access to literature be able to integrate methods and approaches from the different parts of the course in order to solve problems and answer questions within the framework of the course.
- be able to judge which numerical solution method to a given problem best fulfils requirements of speed and exactness.
- with access to literature be able to write Matlab programs for the solution of mathematical problems within the course.
- orally and in writing, with clear logic and with proper terminology be able to explain the solution to a mathematical problem within the course.
- with access to the resources of a library be able independently to assimilate and sum up the contents of a text in technology in which matrix theoretical methods are used.

Matrices and determinants. Linear spaces. Spectral theory.The Jordan normal form. Matrix factorizations. Matrix polynomials and matrix functions. Norms. Scalar products. Singular values. Normal matrices. Quadratic and Hermitian forms. The Least Squares method and pseudo inverses. Some application in numerical analysis.

Grading scale: TH

Assessment: Written and/or oral test, to be decided by the examiner. Two minor computer projects should be completed before the exam.

Required prior knowledge: FMAF05 Systems and Transforms, or similar.

The number of participants is limited to: No

The course overlaps following course/s: FMA121

- Holst, A & Ufnarovski, V: Matrix Theory. Studentlitteratur, 2014, ISBN: xx. A new edition of the current compendium from August 2013 will appear as a book in August 2014.

Course coordinator: Studierektor Anders Holst, Studierektor@math.lth.se

Course homepage: http://www.ctr.maths.lu.se/course/matris/