Linear Algebra


Content, progress and pedagogy of the module

Learning objectives


  • Vectors, matrices and systems of linear equations
  • Connections between solution of systems of linear equations, associated matrices and operations on those
  • Linear independence and dimension. Eigenvalues and eigenvectors
  • The connection between properties of a matrix and of the echelon form of it
  • The connection between a vector space of dimension n and Rn
  • Orthogonality and orthonormal bases


  • Matrix-vector product, product and sum of matrices. Row operations. Gauss elimination.
  • Eigenvalues and eigenspaces.
  • Solution of a system of linear equations on vector form.
  • Bases of subspaces associated with a matrice.
  • Given a basis for a vector space finding coordinates for vectors and the matrix of a linear map.
  • Gram Schmidt, projection on a subspace, projection matrices. Coordinates for a vector wrt. an orthonormal basis.


Can apply methods and concepts from linear algebra, including vector spaces and orthonormal bases to given problems relevant to the study programme.

Type of instruction

Lectures, exercises, videos, quiz, digitalised self-study, workshops on calculus problems relevant to the study programme.

Extent and expected workload

Since it is a 5 ECTS course, the work load is expected to be 150 hours for the student.



Name of examLinear Algebra
Type of exam
Written or oral exam
Permitted aidsPlease see the semester description / module description
Assessment7-point grading scale
Type of gradingInternal examination
Criteria of assessmentThe criteria of assessment are stated in the Examination Policies and Procedures

Facts about the module

Danish titleLineær algebra
Module codeMAT2LIAL1234
Module typeCourse
Duration1 semester
SemesterSpring and Autumn
Language of instructionDanish and English
Empty-place SchemeYes
Location of the lectureCampus Aalborg, Campus Esbjerg
Responsible for the module


Study BoardStudy Board of Mathematical Sciences
DepartmentDepartment of Mathematical Sciences
FacultyThe Faculty of Engineering and Science