FMA 120, Matrix Theory, Spring 2012

Last Modified: 2012-09-19

Home Exam:

v.1 2012-04-20 english

Problem 8: The marix A is assumed to be real

P.S. Check out under first several days for eventual typos or other changes. Contact me if something looks inconsistent.

Oral Exam:

Extra chapters for PhD students (choose three of your choice to study):

Rayleigh quotients: [Spanne, end of Ch. 14] or [1, Ch. 8, §§8.1-8.5] or here until 2.3
Location of eigenvalues: [Spanne, Ch. 16] or [4, Ch. 6, §§6.0, 6.1, 6.3]
Kronecker (direct) product: [Spanne, Ch. 17] or [1, Ch. 12, §§12.1-12.5]] or here
Polynomial matrices: [Spanne, Ch. 18] or [1, Ch. 7, §§7.1-7.8 ] or [2, Ch. VI, §§1-6]. May look also here
Positive matrices: [Spanne, Ch. 19] or [3, Ch. 8]
Circulant and Toeplitz matrices: here (Ch. 3-5)

[1] P. Lancaster, M. Tismenetsky, The Theory of Matrices.
[2] F. Gantmacher, Theory of Matrices, Vol.1.
[3] C. Meyer, Matrix Analysis and Applied Linear Algebra.
[4] R. Horn, C. Johnson, Matrix Analysis.

P.S. I have the books if you wish to borrow it.

News:

Book time for the oral exam for times after May 9.

Basic Course: 6 ECTS
Project Course: 6 ECTS + 3 ECTS for an extra project (that should be done during the course and presented afterwards)
PhD Course: 7.5 ECTS for PhD study (extended variant of the course where 3 extra chapters are for self-study)

Kursprogram (swe)
Mål (swe)
Allmän matriskunskap (swe)
Extraprojekt för 9 hp (swe)

Course Content:

The course covers all chapters except 10 of [Holst, Ufnarovski] and two mini-projects of MATLAB programming kind with deadlines being on 27/2 and 26/3 respectively. Those who pass the mini-projects will have a written take-home exam in April. Those who pass the written exam will need to complete it soon after by the oral exam (approx. 40-60 min). During the oral exam the understanding of the most important facts and notions in the course are tested in the first place.

Course responsible:

Andrey Ghulchak, room MH:350, phone 2228546, Office hours: Wednesday 11.00-12.30

Lectures and exercises:

Time table for VT1 and VT2.

Literature in English:

A. Holst, V. Ufnarovski, Matrix Theory, December 2011, KFS.

One can use older editions of the book that has some known missprints (2011.12.15) and is missing answers and solution hints.

Alternative book in Swedish (shorter with less examples):

S.Spanne, Föreläsningar i Matristeori, 1997, KFS.
S.Spanne, Exempel och problemer för öfning i Matristeori, 1996, KFS.

Chapters 1-14 until 14.3.

Mini-projects:

Andrey Ghulchak