Course syllabus

Matristeori
Matrix Theory

FMA120, 6 credits, A (Second Cycle)

Valid for: 2012/13
Decided by: Education Board 1
Date of Decision: 2011-03-23

General Information

Main field: Technology.
Compulsory for: Pi3
Elective for: C4, C4-ssr, D4, D4-bg, D4-ssr, E4, E4-bg, E4-ra, F4, F4-tf, F4-ssr, F4-bs, F4-bg
Language of instruction: The course might be given in English

Aim

The main aim of the course is to convey knowledge about, and familiarity with the use of, concepts and methods from matrix theory and linear algebra which are important in applications within many subjects in technology, science and economy. 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 theoretical ability in mathematical programming.

Learning outcomes

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 able to understand and describe some application of matrix theory within numerical computation algorithms.

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.

Contents

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

Examination details

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.

Admission

Required prior knowledge: FMAF05 Systems and Transforms, or similar.
The number of participants is limited to: No
The course overlaps following course/s: FMA121

Reading list

Contact and other information

Course coordinator: Studierektor Anders Holst, Studierektor@math.lth.se
Course homepage: http://www.maths.lth.se/matematiklth/vitahyllan/vitahyllan.html
Further information: In autumn the course is given in Swedish. In spring the course is given in English if any participant so wishes.