Linear Algebra, 6 credits (TNIU75)

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
6IBYG Civil Engineering, B Sc in Engineering 3 (Autumn 2017) 1 1 Swedish Norrköping o
6KFTL Air Transportation and Logistics, Bachelor's Programme 3 (Autumn 2017) 1 1 Swedish Norrköping o
6KLOG Civic Logistics, Bachelor´s Programme 3 (Autumn 2017) 1 1 Swedish Norrköping o

Main field of study

Mathematics, Applied Mathematics

Course level

First cycle

Advancement level


Course offered for

  • Civil Engineering, B Sc in Engineering
  • Air Transportation and Logistics, Bachelor's Programme
  • Civic Logistics, Bachelor´s Programme

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.

Intended learning outcomes

After completing this course students should be able to:

  • solve systems of linear equations and be able to interpret these solutions geometrically,
  • handle basic geometric objects in two and three dimensions (like points, vectors, lines, planes) and be able to investigate essential relations between these objects,
  • understand the notion of a matrix and master the matrix calculus in order to perform simple matrix operations (like transposition or multiplication of matrices),
  • understand and apply the notion of basis in space and perform the change of basis,
  • give an account for and perform calculations with the help of basic ideas and methods of theory of linear operators including inverse operators, eigenvalues and eigenvectors, diagonalization of operators (spectral theorem) and dimension theorem as well as relate these to the methods and notions from p. 2, 3, and 4.

Course content

Systems of linear equations. Vectors. Matrices. Determinants. Bases. Change of Bases. The scalar product. The cross product. Lines and planes in space. Linear transformations and their compositions. Eigenvalues and eigenvectors of a linear transformation. Diagonalization. Spectral theorem. Kernel and image of a linear operator. Dimension theorem.

Teaching and working methods

The course consists of lectures and tutorials.


KTR1Optional written testU, G0 credits
TEN1Written examinationU, 3, 4, 56 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

Preliminär schemalagd tid: 52 h
Rekommenderad självstudietid: 108 h

Course literature

Kompletterande litteratur

Albertson, F, Lineär algebra med vektorgeometri, Övningsbok
ISBN: 9789144005287Tengstrand, A, Lineär algebra med vektorgeometri
ISBN: 9789144044187

Additional literature


Albertson, F, Lineär algebra med vektorgeometri, Övningsbok

ISBN: 9789144005287

Tengstrand, A, Lineär algebra med vektorgeometri

ISBN: 9789144044187

KTR1 Optional written test U, G 0 credits
TEN1 Written examination U, 3, 4, 5 6 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 

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