Matrix Theory, Minor Course
Matristeori, mindre kurs

FMA121F, 6 högskolepoäng

Gäller från och med: Autumn 2017
Beslutad av: Professor Thomas Johansson
Datum för fastställande: 2017-02-21

Allmänna uppgifter

Avdelning: Mathematics
Kurstyp: Gemensam kurs, avancerad nivå och forskarnivå
Kursen ges även på avancerad nivå med kurskoder: FMA120, FMAN70
Undervisningsspråk: English

Syfte

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.

Mål

Kunskap och förståelse

För godkänd kurs skall doktoranden

• 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.

Färdighet och förmåga

För godkänd kurs skall doktoranden

• 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.

Kursinnehåll

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.

Kurslitteratur

Holst, A. & Ufnarovski, V.: Matrix Theory. 2014. ISBN 9789144100968.

Kursens undervisningsformer

Undervisningsformer: Föreläsningar, övningar

Kursens examination

Examinationsformer: Skriftlig tentamen, muntlig tentamen, inlämningsuppgifter. Written take-home exam. Programming assignments.
Betygsskala: Underkänd, godkänd
Examinator:

Antagningsuppgifter

Förutsatta förkunskaper: FMA420 Linear algebra and FMA430 Calculus in several variables.

Kurstillfällesinformation

Kontaktinformation och övrigt

Kursansvariga:
Hemsida: http://www.maths.lth.se/course/matris/