# MAT1120 – Linear Algebra

## Course content

This course gives a thorough introduction to linear algebra with emphasis on vector spaces, linear maps, spectral theory, orthogonality and applications of this theory. MATLAB is used for illustrations and for solving numerically various problems. MAT1120 is based on, and is a natural continuation of MAT1110 – Calculus and Linear Algebra, and the course is a building block for a number of advanced mathematical courses.

## Learning outcome

After completing the course you

• have applied basic theory for linear systems of equations
• are well acquainted with the definition of general vector spaces, and with important examples of these spaces, such as the usual n-dimensional Euclidean space and different function spaces
• master concepts like subspace and linear independence, and are familiar with natural subspaces associated with matrices
• have a good understanding of the notions of basis and dimension of vector spaces, are accustomed with change of basis and can use coordinate vectors to solve different problems
• are able to find the matrix representation of linear maps relative to different bases
• know the theory of eigenvalues and eigenvectors, and can use this to solve certain systems of differential equations and analyze discrete dynamical systems
• are familiar with inner product spaces, orthogonality and orthogonal projections, and can compute orthogonal bases
• can solve least-squares problems, and apply this to linear models
• know the spectral theorem for symmetric matrices, and can analyze quadratic forms
• can compute the singular value decomposition of a matrix, and know how to use the information it provides
• can solve different linear algebra problems numerically, for instance how to approximate eigenvalues.

Students who are admitted to study programmes at UiO must each semester register which courses and exams they wish to sign up for in Studentweb.

In addition to fulfilling the Higher Education Entrance Qualification, applicants have to meet the following special admission requirements:

• Mathematics R1 (or Mathematics S1 and S2) + R2

And in addition one of these:

• Physics (1+2)

• Chemistry (1+2)

• Biology (1+2)

• Information technology (1+2)

• Geosciences (1+2)

• Technology and theories of research (1+2)

The special admission requirements may also be covered by equivalent studies from Norwegian upper secondary school or by other equivalent studies (in Norwegian).

## Teaching

6 hours of lectures, 2 hours of groups per week throughout the semester.

The number of groups offered can be adjusted during the semester, depending on attendance.

## Examination

Final written exam which counts 100 % towards the final grade.

This course has 2 mandatory assignments that must be approved before you can sit the final exam.

### Examination support material

No examination support material is allowed.

### Language of examination

The examination text is given in Norwegian. You may submit your response in Norwegian, Swedish, Danish or English.

### Resit an examination

This course offers both postponed and resit of examination. Read more:

### Special examination arrangements, use of sources, explanations and appeals

See more about examinations at UiO

Last updated from FS (Common Student System) Nov. 26, 2022 10:49:07 AM

Credits
10
Level
Bachelor
Teaching
Autumn
Examination
Autumn
Teaching language
Norwegian

## Contact

Department of Mathematics