MATB32 Linear Algebra, 7.5 credits, is a compulsory course for a Bachelor of Science degree in mathematics and in physics. The course can be taken as an stand-alone course. The course is given at half-study pace during the first half of each semester. The course is given in English

Course Content
The course treats:

Matrices: matrix operations, matrix inverse, matrix rank
Determinants: definition and properties
Linear spaces: subspace, span, linear dependence/independence, basis, dimension
Euclidean spaces: scalar product, Cauchy-Schwarz inequality, orthogonality, orthonormal bases, orthogonalisation, orthogonal matrices, orthogonal projection, orthogonal complement, least squares method, isometries.
Linear mappings: matrices of linear mappings, kernel and image, composition and inverse, change of basis, rank-nullity theorem
Spectral theory: eigenvalues, eigenvectors, eigenspace, characteristic polynomial, diagonalisability, the spectral theorem
Systems of linear ordinary differential equations.
Quadratic forms: bilinear forms, diagonalisation, quadratic curves, quadratic surfaces, law of inertia

Teaching
The teaching consists of lectures, seminars and, depending on the specialisation of the project, computer exercises. An essential element of the seminars is training in problem solving and oral mathematical communication.
A mandatory project that can consist of a number of problems is included in the course requirements. The project aims to translate mathematical theory into computer programs in order to be able to solve problems that apply the content of the course. The project also aims at providing the students with training in mathematical communication in speech and writing.

Assessment

The examination consists of the following parts:

written and oral presentation of the project during the course (1.5 credits). Grading scale: Fail, Pass
written examination at the end of the course (6 credits) Grading scale: Fail, Pass, Pass with Distinction.

For a Pass grade on the whole course, the student must have Pass grades in the project and in the written examination.
The final grade is determined by the grade in the written examination.

Course Literature

Kjell Elfström, Linear Algebra, 2025

Official Course Description

Syllabus in English
Kursplan på svenska

Course Evaluation
Link to course evaluations on the department's website:

Course Evaluations, Mathematics at Faculty of Science