## Admission requirements

none

## Description

This course covers the basic concepts of linear algebra. We will treat several abstract concepts and structures from linear algebra, and also the relevant calculation techniques and a number of applications.

The following subjects will be covered:

1. Vectors: addition, scalar multiplication, inner product.

2. Solution of systems of linear equations using Gaussian elimination.

3. Matrices and determinants.

4. Vector geometry in Rn.

5. General vector spaces, linear subspaces, linear maps, change of basis.

6. Eigenvalues and eigenvectors, diagonalisation.

## Course Objectives

In this course you will learn to work with vectors, matrices, determinants, eigenvalues and eigenvectors. You will also learn the concepts of an abstract vector space and a linear map, and how to prove theorems about these objects.

## Mode of instruction

Lectures, exercise classes and homework.

## Assessment method

The final grade consists of homework (20%), a written mid-term exam (20%) and a written final (resit) exam (60%). To pass the course, the grade for the final (resit) exam must be at least 5 and the (unrounded) weighted average of the three components at least 5.5. There is no minimum requirement for homework in order to sit the exam or to pass the course. The homework and mid-term exam cannot be retaken. * The homework counts as a practical exercise and consists of 12 assignments, for which the lowest two grades do not count towards the final grade. * The mid-term exam counts as a partial exam. The grade will be replaced by that of the final (resit) exam if the latter is higher.

## Literature

Lecture notes “Linear Algebra I” by Ronald van Luijk and Michael Stoll (available online, or for sale via the MI administration).

## Brightspace

All information about this course will be available on the course’s Brightspace page.

## Contact information

m.j.bright[at]math.leidenuniv.nl