Linear Algebra, 6 credits

Linjär algebra, 6 hp


Main field of study

Mathematics Applied Mathematics

Course level

First cycle

Course type

Programme course


George Baravdish

Course coordinator

George Baravdish

Director of studies or equivalent

George Baravdish

Education components

Preliminary scheduled hours: 87 h
Recommended self-study hours: 73 h
ECV = Elective / Compulsory / Voluntary
Course offered for Semester Period Timetable module Language Campus ECV
6CKTS Communications, Transport and Infrastructure, Master of Science in Engineering 1 (Autumn 2018) 2 - Swedish Norrköping, Norrköping C
6CIEN Electronics Design Engineering, Master of Science in Engineering 1 (Autumn 2018) 2 - Swedish Norrköping, Norrköping C
6CMEN Media Technology and Engineering, Master of Science in Engineering 1 (Autumn 2018) 2 - Swedish Norrköping, Norrköping C

Main field of study

Mathematics, Applied Mathematics

Course level

First cycle

Advancement level


Course offered for

  • Master of Science in Electronics Design Engineering
  • Master of Science in Communications, Transport and Infrastructure
  • Master of Science in Media Technology and 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.


    KTR2Individual assignments0 creditsD
    UPG2Individual assignment0 creditsU, G
    KTR1Individual assignments0 creditsD
    TEN1Written examination6 creditsU, 3, 4, 5


    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


    • Kompendium utgivet vid ITN.
  • Code Name Scope Grading scale
    KTR2 Individual assignments 0 credits D
    UPG2 Individual assignment 0 credits U, G
    KTR1 Individual assignments 0 credits D
    TEN1 Written examination 6 credits U, 3, 4, 5

    Course syllabus

    A syllabus has been established for each course. The syllabus specifies the aim and contents of the course, and the prior knowledge that a student must have in order to be able to benefit from the course.


    Courses are timetabled after a decision has been made for this course concerning its assignment to a timetable module. A central timetable is not drawn up for courses with fewer than five participants. Most project courses do not have a central timetable.

    Interrupting a course

    The vice-chancellor’s decision concerning regulations for registration, deregistration and reporting results (Dnr LiU-2015-01241) states that interruptions in study are to be recorded in Ladok. Thus, all students who do not participate in a course for which they have registered must record the interruption, such that the registration on the course can be removed. Deregistration from a course is carried out using a web-based form: 

    Cancelled courses

    Courses with few participants (fewer than 10) may be cancelled or organised in a manner that differs from that stated in the course syllabus. The board of studies is to deliberate and decide whether a course is to be cancelled or changed from the course syllabus. 

    Regulations relating to examinations and examiners 

    Details are given in a decision in the university’s rule book:

    Forms of examination


    Written and oral examinations are held at least three times a year: once immediately after the end of the course, once in August, and once (usually) in one of the re-examination periods. Examinations held at other times are to follow a decision of the board of studies.

    Principles for examination scheduling for courses that follow the study periods:

    • courses given in VT1 are examined for the first time in March, with re-examination in June and August
    • courses given in VT2 are examined for the first time in May, with re-examination in August and October
    • courses given in HT1 are examined for the first time in October, with re-examination in January and August
    • courses given in HT2 are examined for the first time in January, with re-examination at Easter and in August.

    The examination schedule is based on the structure of timetable modules, but there may be deviations from this, mainly in the case of courses that are studied and examined for several programmes and in lower grades (i.e. 1 and 2). 

    • Examinations for courses that the board of studies has decided are to be held in alternate years are held only three times during the year in which the course is given.
    • Examinations for courses that are cancelled or rescheduled such that they are not given in one or several years are held three times during the year that immediately follows the course, with examination scheduling that corresponds to the scheduling that was in force before the course was cancelled or rescheduled.
    • If teaching is no longer given for a course, three examination occurrences are held during the immediately subsequent year, while examinations are at the same time held for any replacement course that is given, or alternatively in association with other re-examination opportunities. Furthermore, an examination is held on one further occasion during the next subsequent year, unless the board of studies determines otherwise.
    • If a course is given during several periods of the year (for programmes, or on different occasions for different programmes) the board or boards of studies determine together the scheduling and frequency of re-examination occasions.

    Registration for examination

    In order to take an examination, a student must register in advance at the Student Portal during the registration period, which opens 30 days before the date of the examination and closes 10 days before it. Candidates are informed of the location of the examination by email, four days in advance. Students who have not registered for an examination run the risk of being refused admittance to the examination, if space is not available.

    Symbols used in the examination registration system:

      ** denotes that the examination is being given for the penultimate time.

      * denotes that the examination is being given for the last time.

    Code of conduct for students during examinations

    Details are given in a decision in the university’s rule book:

    Retakes for higher grade

    Students at the Institute of Technology at LiU have the right to retake written examinations and computer-based examinations in an attempt to achieve a higher grade. This is valid for all examination components with code “TEN” and "DAT". The same right may not be exercised for other examination components, unless otherwise specified in the course syllabus.

    Retakes of other forms of examination

    Regulations concerning retakes of other forms of examination than written examinations and computer-based examinations are given in the LiU regulations for examinations and examiners,


    For examinations that involve the writing of reports, in cases in which it can be assumed that the student has had access to other sources (such as during project work, writing essays, etc.), the material submitted must be prepared in accordance with principles for acceptable practice when referring to sources (references or quotations for which the source is specified) when the text, images, ideas, data, etc. of other people are used. It is also to be made clear whether the author has reused his or her own text, images, ideas, data, etc. from previous examinations.

    A failure to specify such sources may be regarded as attempted deception during examination.

    Attempts to cheat

    In the event of a suspected attempt by a student to cheat during an examination, or when study performance is to be assessed as specified in Chapter 10 of the Higher Education Ordinance, the examiner is to report this to the disciplinary board of the university. Possible consequences for the student are suspension from study and a formal warning. More information is available at


    The grades that are preferably to be used are Fail (U), Pass (3), Pass not without distinction (4) and Pass with distinction (5). Courses under the auspices of the faculty board of the Faculty of Science and Engineering (Institute of Technology) are to be given special attention in this regard.

    1. Grades U, 3, 4, 5 are to be awarded for courses that have written examinations.
    2. Grades Fail (U) and Pass (G) may be awarded for courses with a large degree of practical components such as laboratory work, project work and group work.

    Examination components

    1. Grades U, 3, 4, 5 are to be awarded for written examinations (TEN).
    2. Grades Fail (U) and Pass (G) are to be used for undergraduate projects and other independent work.
    3. Examination components for which the grades Fail (U) and Pass (G) may be awarded are laboratory work (LAB), project work (PRA), preparatory written examination (KTR), oral examination (MUN), computer-based examination (DAT), home assignment (HEM), and assignment (UPG).
    4. Students receive grades either Fail (U) or Pass (G) for other examination components in which the examination criteria are satisfied principally through active attendance such as other examination (ANN), tutorial group (BAS) or examination item (MOM).

    The examination results for a student are reported at the relevant department.

    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 


    Kompendium utgivet vid ITN.

    Note: The course matrix might contain more information in Swedish.

    I = Introduce, U = Teach, A = Utilize
    I U A Modules Comment
    1.1 Knowledge of underlying mathematics and science (G1X level)
    1.2 Fundamental engineering knowledge (G1X level)
    1.3 Further knowledge, methods, and tools in one or several subjects in engineering or natural science (G2X level)
    1.4 Advanced knowledge, methods, and tools in one or several subjects in engineering or natural sciences (A1X level)
    1.5 Insight into current research and development work
    2.1 Analytical reasoning and problem solving
    2.2 Experimentation, investigation, and knowledge discovery
    2.3 System thinking
    2.4 Attitudes, thought, and learning
    2.5 Ethics, equity, and other responsibilities
    3.1 Teamwork
    3.2 Communications
    3.3 Communication in foreign languages
    4.1 External, societal, and environmental context
    4.2 Enterprise and business context
    4.3 Conceiving, system engineering and management
    4.4 Designing
    4.5 Implementing
    4.6 Operating
    5.1 Societal conditions, including economic, social, and ecological aspects of sustainable development for knowledge development
    5.2 Economic conditions for knowledge development
    5.3 Identification of needs, structuring and planning of research or development projects
    5.4 Execution of research or development projects
    5.5 Presentation and evaluation of research or development projects

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