Course Syllabus for

Matrix Theory

FMA122F, 7.5 credits

Valid from: Autumn 2019
Decided by: FN1/Anders Gustafsson
Date of establishment: 2014-04-22

General Information

Division: Mathematics
Course type: Third-cycle course
Teaching language: English


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 mathematics and, e.g., control theory.


Knowledge and Understanding

For a passing grade the doctoral student must

Competences and Skills

For a passing grade the doctoral student must

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. Direct products of Matrices. Matrices with polynomial elements. Non-negative matrices.

Course Literature

The book covers the part of the course which coincides with the second cycle course. For postgraduate students additional material will be provided. Both editions work.

Instruction Details

Types of instruction: Lectures, exercises

Examination Details

Examination formats: Written exam, oral exam, written assignments. The assignments are two minor programming exercises in Matlab and Maple, respectively.
Grading scale: Failed, pass

Admission Details

Further Information

The tertiary course coincides with the secondary course FMA120/FMAN70 Matrix theory except that the tertiary course also encompasses three subjects which the doctoral student may choose from five alternatives. Replaces FMA120F.

Course Occasion Information

Contact and Other Information

Course coordinators:

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