# MAT1120 - Linear algebra

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## Course content

MAT1120 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, and the course is a building block for a number of advanced mathematical  courses.

## Learning outcome

After having completed the course:

• you have applied basic theory for linear systems of equations
• you 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
• you master concepts like subspace and linear independence, and are  familiar with natural subspaces associated with matrices
• you 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
• you are able to find the matrix representation of linear maps relative to different bases
• you know the theory of eigenvalues and eigenvectors, and can use this to solve certain systems of differential equations and analyze discrete dynamical systems
• you are familiar with inner product spaces, orthogonality and orthogonal projections, and can compute orthogonal bases
• you can solve least-squares problems, and apply this to linear models
• you know the spectral theorem for symmetric matrices, and can analyze quadratic forms
• you can compute the singular value decomposition of a matrix, and know how to use the information it provides
• you 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.

## Prerequisites

### Formal prerequisite knowledge

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

One of these:

• Mathematics R1
• Mathematics (S1+S2)

And and in addition one of these:

• Mathematics (R1+R2)
• 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. Read more about special admission requirements (in Norwegian).

## Overlapping courses

10 credits with MAT120. 9 credits against MA103. 10 credits against MA104. 6 credits against MA113. 10 credits against MA114.

## Teaching

4 hours of lectures, 2 hours of problem session in plenum and 2 hours exercises per week.

## Examination

Two compulsory project assignments need to be passed within given deadlines to be allowed to take the final exam. Final mark based on written examination at the end of the semester.

Permittes aids at the exam: None.

### Language of examination

Subjects taught in English will only offer the exam paper in English.

You may write your examination paper in Norwegian, Swedish, Danish or English.

### Resit an examination

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

### Withdrawal from an examination

It is possible to take the exam up to 3 times. If you withdraw from the exam after the deadline or during the exam, this will be counted as an examination attempt.

### Special examination arrangements

Application form, deadline and requirements for special examination arrangements.

## Evaluation

The course is subject to continuous evaluation. At regular intervals we also ask students to participate in a more comprehensive evaluation.

10

Bachelor

Every autumn

Every autumn

Norwegian

## Contact

Department of Mathematics