(Created 2010-07-25.)

MATRIX THEORY | FMA120 |

**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.

*Knowledge and understanding*

For a passing grade the 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 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

be able to judge which numerical solution method to a given problem best fulfils requirements on 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. 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**

Holst, A, Ufnarovsky, V: Matrix Theory. Matematikcentrum, 2009.