Linear Algebra, 6 credits (TNA002)

Linjär algebra, 6 hp

Main field of study

Mathematics Applied Mathematics


First cycle

Course type

Programme course


George Baravdish

Director of studies or equivalent

George Baravdish
Course offered for Semester Period Timetable module Language Campus VOF
6CIEN Electronics Design Engineering, M Sc in Engineering 1 (Autumn 2017) 2 - Swedish Norrköping o
6CKTS Communications, Transport and Infrastructure, M Sc in Engineering 1 (Autumn 2017) 2 - Swedish Norrköping o
6CMEN Media Technology and Engineering, M Sc in Engineering 1 (Autumn 2017) 2 - Swedish Norrköping o

Main field of study

Mathematics, Applied Mathematics

Course level

First cycle

Advancement level


Course offered for

  • Electronics Design Engineering, M Sc in Engineering
  • Communications, Transport and Infrastructure, M Sc in Engineering
  • Media Technology and Engineering, M Sc in Engineering

Entry requirements

Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshold requirements for progression within the programme, or corresponding.


Foundadtion course in mathematics

Intended learning outcomes

To give a unified framework for geometrical and algebraic techniques, with applications in analysis, mechanics, computer graphics, numerical analysis, mathematical statistics, control theory, linear optimization and other subjects. It is also included to develop the ability of using the mathematical language both written and oral. It is necessary for the participant to be able to

  • solve systems of linear equations
  • work with inner and cross product
  • calculate with matrices and determinants
  • calculate with vectors and coordinates in a vector space
  • determine the matrix for a linear transformation and the kernel and the range for such matrices
  • determine ON-basis in an inner product space
  • do orthogonal projection on subspaces and to use least squares approximations
  • solve problems by changing basis
  • determine and to use eigenvalues and eigenvectors in different problems
  • use the spectral theorem in different problems
  • determine the canonical basis of quadratic forms and to use these to solve geometrical problems.
  • carry out inspections of results and partial results, in order to verify that these are correct or reasonable
  • solve system of linear ordinary differential equations

  • Course content

    Vectors, straight lines and planes. Linear systems of equations. Matrices and determinants. Vector spaces. Euclidean spaces.
    Linear mappings. Isometric and symmetric mappings. Eigenvalues and eigenvectors. Diagonalization. Otrhogonality. Quadratic forms. Distance and approximation. System of linear ordinary differential equations

    Teaching and working methods

    The course is given in the form of lectures and tutorials.


    TEN1Written examinationU, 3, 4, 56 credits
    KTR1Individual assignmentsD0 credits
    UPG2Individual assignmentU, G0 credits
    KTR2Individual assignmentsD0 credits


    Four-grade scale, LiU, U, 3, 4, 5


    Institutionen för teknik och naturvetenskap

    Director of Studies or equivalent

    George Baravdish


    George Baravdish

    Course website and other links

    Education components

    Preliminary scheduled hours: 87 h
    Recommended self-study hours: 73 h

    Course literature

    Additional literature


    Kompendium utgivet vid ITN.

    Additional literature


    Kompendium utgivet vid ITN.

    TEN1 Written examination U, 3, 4, 5 6 credits
    KTR1 Individual assignments D 0 credits
    UPG2 Individual assignment U, G 0 credits
    KTR2 Individual assignments D 0 credits

    Regulations (apply to LiU in its entirety)

    The university is a government agency whose operations are regulated by legislation and ordinances, which include the Higher Education Act and the Higher Education Ordinance. In addition to legislation and ordinances, operations are subject to several policy documents. The Linköping University rule book collects currently valid decisions of a regulatory nature taken by the university board, the vice-chancellor and faculty/department boards.

    LiU’s rule book for education at first-cycle and second-cycle levels is available at 

    This tab contains public material from the course room in Lisam. The information published here is not legally binding, such material can be found under the other tabs on this page. There are no files available for this course.

    Page responsible: Info Centre,