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# Details for the Course Syllabus for Course FMA121F valid from Autumn 2017

General
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.
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.
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.
Judgement and Approach
• For a passing grade the doctoral student must
Types of Instruction
• Lectures
• Exercises
Examination Formats
• Written exam
• Oral exam
• Written assignments
• Written take-home exam. Programming assignments.
• Failed, pass
Assumed Prior Knowledge
• FMA420 Linear algebra and FMA430 Calculus in several variables.
Selection Criteria
Literature
• Holst, A. & Ufnarovski, V.: Matrix Theory. 2014. ISBN 9789144100968.
Further Information
Course code
• FMA121F