Syllabus academic year 2007/2008
 MATRIX THEORY FMA120

Higher education credits: 6. Grading scale: TH. Level: A (Second level). Language of instruction: The course will be given in Swedish. FMA120 overlap following cours/es: FMA121 och FMA121. Compulsory for: Pi3. Optional for: C4, C4sst, D3, D3bg, D3sst, E3bg, E3ra, F3, F3rs, F3sfm, F3tmb, F3tvb, I3, L4, M3. Course coordinator: Director of Studies Lars Christer Böiers, Lars_Christer.Boiers@math.lth.se, Matematik. Recommended prerequisits: FMA036 Linear Analysis or similar. Assessment: Written and/or oral test, to be decided by the examiner. Three minor projects should be completed before the exam. Home page: http://www.maths.lth.se/matematiklth/vitahyllan/vitahyllan.html.

Aim
The major 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.

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.

Skills and abilities
For a passing grade the student must

with access to literature be able to integrate methods and views 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 that best fulfils requirements on speediness and exactness.

with access to literature be able to write Matlab programs for the solution av 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. 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.

Literature
Spanne, S: Matristeori. KF-Sigma 1994.
Supplementary material.