MA6202 - Linear Algebra with Applications


Examination arrangement

Examination arrangement: Home examination
Grade: Letters

Evaluation form Weighting Duration Examination aids Grade deviation
Home examination 100/100 4 hours

Course content

The course is a continuation of MA6201.

This course corresponds scientifically to MA1202, adapted to Continuing Education.

We start with general vector spaces over the real and complex numbers, and linear maps (including related subspaces – kernel and image – and representations in matrix form given bases). We study operators on finite dimensional vector spaces by looking at eigenvectors, eigenspaces, generalized eigenspaces, aiming for the Cayley-Hamilton theorem and normal forms.

Inner product spaces are a concept generalizing the dot product. Studying these, both over the real and complex numbers, is an important part of this course. Orthogonal bases are constructed by using the Gram Schmidt algorithm. Then various types of operators on inner product spaces are studied (orthogonal, real symmetric, unitary, normal, self-adjoint), including the corresponding matrices.

The course can contain more advanced concepts from linear algebra, such as dual spaces, bilinear forms and quotient spaces.

Several applications are illustrated; these may vary from year to year. Examples: Markov chains, population growth (Leslie matrices), game theory, systems of differential equations, Fourier analysis, and fractals.

Learning outcome

1. Knowledge. The student is familiar with basic concepts concerning general vector spaces, matrices and linear transformations as discussed above. The student is familiar with several applications of linear algebra.

2. Skills. The student masters various algorithms and methods to make calculations involving vector spaces, inner product spaces, and linear transformations. Central skills are applying the Gram-Schmidt algorithm, finding eigenspaces, diagonalizing matrices, and applications varying from year to year. The student is able to write simple mathematical proofs.

Learning methods and activities

Lectures, exercises, gatherings, and a final written exam.

Compulsory assignments

  • Exercises

Specific conditions

Exam registration requires that class registration is approved in the same semester. Compulsory activities from previous semester may be approved by the department.

Admission to a programme of study is required:
Mathematics, distance learning (FUMA)

Course materials

Will be announced at the start of the semester.

Credit reductions

Course code Reduction From To
MA1202 7.5 01.09.2007
TMA4110 3.0 01.09.2020
More on the course



Version: 1
Credits:  7.5 SP
Study level: Further education, lower degree level


Term no.: 1
Teaching semester:  SPRING 2021

Language of instruction: -

Location: Trondheim

Subject area(s)
  • Mathematics
Contact information
Course coordinator:

Department with academic responsibility
Department of Mathematical Sciences

Department with administrative responsibility
Centre for Continuing Education and Professional Development



Examination arrangement: Home examination

Term Status code Evaluation form Weighting Examination aids Date Time Digital exam Room *
Summer UTS Home examination 100/100 INSPERA
Room Building Number of candidates
Spring ORD Home examination 100/100

Release 2021-06-09

Submission 2021-06-09

Release 09:00

Submission 13:00

Room Building Number of candidates
  • * The location (room) for a written examination is published 3 days before examination date. If more than one room is listed, you will find your room at Studentweb.

For more information regarding registration for examination and examination procedures, see "Innsida - Exams"

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