Linear Algebra II, 7.5 credits

Learning outcomes

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

• use central concepts from abstract algebra on vector spaces and linear maps.

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

• using algebraic proof methods to prove statements in linear algebra,
• formulate and use the most important theorems in linear algebra,
• describe solutions to problems in linear algebra in a logically coherent and mathematically correct way, and
• solve problems in linear algebra using computer tools.

Evaluation Ability and Approach
After completed studies the student shall be able to

• choose a suitable method for solving problems in linear algebra as well as be able to argue for the choice of method.

Content

Complex vector spaces, inner product spaces, QR factorization and the method of least squares, diagonalization and quadratic forms, linear transformations, canonical forms, singular value decomposition, LU factorization, quotient spaces and the isomorphism theorem, direct sum, linear forms and the algebraic dual, the tensor product.

Examinations and grades

Theory and Problem Solving, 6 credits (Code: A001)
Grades used are Fail (F), Sufficient (E), Satisfactory (D), Good (C), Very Good (B) or Excellent (A).

Computer-Aided Calculations, 1.5 credits (Code: A002)
Grades used are Fail (U) or Pass (G).

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).

Comments on grades

The final course grade is given as the grade for the examination component Theory and problem solving, provided that the grade for the examination component Computer-aided calculations is Passed.

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

Multivariate Calculus, 9 credits and Abstract Algebra, 7.5 credits.

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

Other provisions

All or part of the course may be given in English.

If the course has only a few registered participants, the above-described teaching methods can be completely or partially replaced by supervision and self-study.

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

Material handed out by the Department of Mathematics.