Matrix Theory
Matristeori

FMA120F, 7.5 högskolepoäng

Gäller från och med: Autumn 2013
Beslutad av: FN1/Anders Gustafsson
Datum för fastställande: 2014-04-22

Allmänna uppgifter

Avdelning: Mathematics
Kurstyp: Ren forskarutbildningskurs
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 mathematics and, e.g., control theory.

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 familiar with 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.
• 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.

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

Kurslitteratur

• math-aho & math-vuf: Matrix Theory. KFS, 2013.
• math-aho & math-vuf: Matrix Theory. Studentlitteratur, 2014.

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.

Kursens undervisningsformer

Undervisningsformer: Föreläsningar, övningar

Kursens examination

Examinationsformer: Skriftlig tentamen, muntlig tentamen, inlämningsuppgifter. The assignments are two minor programming exercises in Matlab and Maple, respectively.
Betygsskala: Underkänd, godkänd
Examinator:

Antagningsuppgifter

Övrig information

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

Kurstillfällesinformation

Kontaktinformation och övrigt

Kursansvariga: