Matrix Analysis and Perturbation Theory, 7.5 credits

Learning outcomes

Knowledge and Understanding
After completed studies, the student shall be able to

• account for the main results in matrix analysis and perturbation theory and how they are used in various applications.

Competence and Skills
After completed studies, the student shall be able to

• use the techniques of matrix analysis and perturbation theory to analyze and solve matrix equations,
• use the methods of matrix analysis and perturbation theory to factorize matrices, and
• solve and analyze generalized and polynomial eigenvalue problems.

Content

Matrix equations. Canonical forms. Matrices with structures. Decompositions of matrices. Perturbation of eigenvalues. Generalized and polynomial eigenvalue problems. Applications.

Examinations and grades

Examination, 7.5 credits (Code: A001)
Grades used are Fail (F), Sufficient (E), Satisfactory (D), Good (C), Very Good (B) or Excellent (A).

According to the Higher Education Ordinance, Chapter 6, Section 18, a grade is to be awarded on the completion of a course, unless otherwise prescribed by the university. The university may determine which grading system is to be used. The grade must be determined by a teacher specifically nominated by the university (the examiner).

In accordance with university regulations on grading systems for first and second-cycle courses and study programmes (Vice-Chancellor’s decision ORU 2018/00929), one of the following grades is to be used: fail (U), pass (G) or pass with distinction (VG). For courses included in an international master’s programme (60 or 120 credits) or offered to the university’s incoming exchange students, the A to F grading scale is to be used. The vice-chancellor, or a person appointed by them, may decide on exceptions from this provision for a specific course, if there are special grounds for doing so.

The grades used on this course are Fail (F), Sufficient (E), Satisfactory (D), Good (C), Very Good (B) or Excellent (A).

Modes of assessment

• Examination (code A001): Written assignments

For students with a documented disability, the university may approve applications for adapted or other modes of assessment.

For further information, see the university's local examination regulations.

Specific entry requirements

Computational Mathematics II, 7.5 credits, and Linear Algebra II, 7.5 credits

For further information, see the university's admission regulations.

Other provisions

The course will be given in English.

Students who have been admitted to and registered on a course have the right to receive tuition and/or supervision for the duration of the time period specified for the particular course to which they were accepted (see, the university's admission regulations (in Swedish)). After that, the right to receive tuition and/or supervision expires.

Reading list and other learning resources

Required Reading

Horn, Roger A., and Johnson, Charles R. (2013)
Matrix analysis
Cambridge University Press

Stewart, Gilbert W., and Sun, Ji-guang (1990)
Matrix Perturbation Theory
Academic Press