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SF1681 Linear Algebra. Advanced Course 6.0 credits

Choose semester and course offering

Choose semester and course offering to see current information and more about the course, such as course syllabus, study period, and application information.


For course offering

Autumn 2024 Start 28 Oct 2024 programme students

Application code


Headings with content from the Course syllabus SF1681 (Autumn 2019–) are denoted with an asterisk ( )

Content and learning outcomes

Course contents

Vector spaces, linear transformations, bases, direct sums, eigenvalues and generalized eigenvectors, Jordan canonical form, inner product spaces, adjoint, Hermitian and unitary operators, singular value decomposition, tensor products, outer product and finite groups, with applications in, for example, differential equations, signal analysis, inverse problems, linear regression, image compression, Markov chains or graph theory.

Intended learning outcomes

After completing the course students should for a passing grade be able to

  • Explain the meaning of basic concepts and theorems within the parts of linear algebra as described by the course content.
  • Use basic concepts and theorems within the parts of linear algebra as described by the course content in order to solve applied problems and to communicate with the help of mathematical terminology also in other contexts.

For higher grades, the student should in addition be able to

  • Explain how different theorems and concepts are connected and deduce relationships from the given theorems.

Literature and preparations

Specific prerequisites

Completed basic course SF1672 Linear Algebra or SF1624 Algebra and Geometry.

Recommended prerequisites

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Announced no later than 4 weeks before the start of the course on the course web page.

Examination and completion

If the course is discontinued, students may request to be examined during the following two academic years.

Grading scale

A, B, C, D, E, FX, F


  • TEN1 - Exam, 6.0 credits, grading scale: A, B, C, D, E, FX, F

Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.

The examiner may apply another examination format when re-examining individual students.

The examiner decides, in consultation with KTHs Coordinator of students with disabilities (Funka), about any customized examination for students with documented, lasting disability. The examiner may allow another form of examination for re-examination of individual students.

Opportunity to complete the requirements via supplementary examination

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Opportunity to raise an approved grade via renewed examination

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Ethical approach

  • All members of a group are responsible for the group's work.
  • In any assessment, every student shall honestly disclose any help received and sources used.
  • In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.

Further information

Course room in Canvas

Registered students find further information about the implementation of the course in the course room in Canvas. A link to the course room can be found under the tab Studies in the Personal menu at the start of the course.

Offered by

Main field of study


Education cycle

First cycle

Add-on studies

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