Course Syllabus for

# Matrix Theory, Minor Course Matristeori, mindre kurs

## FMA121F, 6 credits

Valid from: Autumn 2017
Decided by: Professor Thomas Johansson
Date of establishment: 2017-02-21

## General Information

Division: Mathematics
Course type: Course given jointly for second and third cycle
The course is also given at second-cycle level with course codes: FMA120, FMAN70
Teaching language: English

## Aim

The aim of the course is to give knowledge about the structure of finite dimensional linear maps, and their representing matrices, which is necessary for research in e.g. mechanics.

## Goals

Knowledge and Understanding

For a passing grade the doctoral student must

• 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 with as well as without computer support.
• be able to describe the common classes of normal matrices and their properties.

Competences and Skills

For a passing grade the doctoral student must

• independently be able to characterize and use different types of matrix factorizations.
• 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.

## Course Contents

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.

## Course Literature

Holst, A. & Ufnarovski, V.: Matrix Theory. 2014. ISBN 9789144100968.

## Instruction Details

Types of instruction: Lectures, exercises

## Examination Details

Examination formats: Written exam, oral exam, written assignments. Written take-home exam. Programming assignments.