Course syllabus

Lineär algebra
Linear Algebra

FMAB22, 7,5 credits, G1 (First Cycle)

Valid for: 2023/24
Faculty: Faculty of Engineering, LTH
Decided by: PLED F/Pi
Date of Decision: 2023-04-18

General Information

Main field: Technology.
Compulsory for: F1, Pi1
Language of instruction: The course will be given in Swedish


The course is a basic introduction to linear algebra with the aim of giving the future engineer the knowledge and skills that are required for further studies in mathematic, statistics, physics and other quantitative subjects.

Particular emphasis is put on developping the mathematical theory in a systematic manner starting with the axioms for vector spaces, and in this way contributing to the further aims of enhancing the students' ability to assimilate mathematical text, to carry out a mathematical reasoning, to solve problems of both theoretical and applied character, and to communicate mathematics.

Learning outcomes

Knowledge and understanding
For a passing grade the student must

Competences and skills
For a passing grade the student must

Judgement and approach
For a passing grade the student must


Mathematical induction.

Systems of linear equations and Gaussian elimination.

Geometric vectors in two and three dimensions. Linear independence, bases and coordinate systems. Equations for lines and planes. Conic sections: ellipses, parabolas and hyperbolas. Scalar and vector products with applications.

Matrices and matrix algebra. Matrix inverse and rank. Matrix factorizations such as LU, QR and Cholesky faktorizations.

Abstract vector spaces, bases and coordinates, dimension, subspace. Linear mappings and their representations with matrices, projections, reflections and rotations. Kernel and range for a linear mapping. The Rank-Nullity Theorem.

Inner product spaces, orthogonal complement, orthogonal projections, isometries and orthogonal matrices.The method of least squares with applications.

Determinants. Eigenvalues and eigenvectors. Change of basis and diagonalization. The spectral theorem for symmetric maps on finite dimensional spaces .

Examination details

Grading scale: TH - (U,3,4,5) - (Fail, Three, Four, Five)
Assessment: Assignment, written and oral presentation of the solution to a problem that the student has been given in advance. Written examination comprising theory and problems. The student must have passed on the assignment in order to be eligible to take part in the examination.

The examiner, in consultation with Disability Support Services, may deviate from the regular form of examination in order to provide a permanently disabled student with a form of examination equivalent to that of a student without a disability.

Code: 0123. Name: Linear Algebra.
Credits: 7,5. Grading scale: TH. Assessment: Written examination comprising theory and problems. Further information: The student must have passed on the assignment (oral and in writing) in order to take the written examination.
Code: 0223. Name: Assignment.
Credits: 0. Grading scale: UG. Contents: When the assignment is examined the student must bring a written solution to a previously distributed problem connected with the course contents. He or she must be able to orally account for the solution, and answer questions about it. Further information: Apart from the scheduled session to pass on the assignment there are a few extra chances, for those who need them, to pass before the written examination on the course.


The number of participants is limited to: No
The course overlaps following course/s: FMAA20, FMAA21, FMAB20, MATA22, FMA420

Reading list

Contact and other information

Director of studies: Anders Holst,
Teacher: Tomas Persson,
Course administrator: Studerandeexpeditionen,
Course homepage: