Learning outcomes

This course provides an introduction to linear algebra theory and matrix computations. It will present the main concepts in algebra (vector space, metric space, bases, matrices, projections), along with the associated results and proofs.

Goals

With this course, the student will become familiar with linear algebra theory, and will be able to draw connections with geometry (algebra and analytic geometry - SMATB107). By the end of the course, the student will know the main concepts and results in linear algebra as well some results. This will provide a good basis for her/his subsequent curriculum as mathematician or physicist.

 

 

 

Content

We first describe algebraic structures and present the notions of bases, vector subspaces, linear applications, matrices and their eigenstructure. Then we introduce metric spaces and conclude with matrix norms and projections.

Table of contents

1. Algebraic structures

2. Bases and dimension

3. Vector subspaces

4. Matrices

5. Eigenstructure

6. Metric space

7. matrix norms

8. Projections and generalized inverse

 

Exercices

The exercices are given in parallel with the course and are supervised by a teaching assistant.

Assessment method

Written exam (3 hours) in two parts: theory (results, proofs, and understanding of the concepts) and exercices (application of theoretical results). The final grade is the exam grade. It will be increased by one unit (on a scale from 0 to 20) if the exam grade is greater or equal to 10/20 and if the group project is evaluated with a grade greater or equal to 15/20.

Sources, references and any support material

Two manuscripts (lecture notes and book of exercices) are available.

Language of instruction

Français
Training Study programme Block Credits Mandatory
Bachelor in Mathematics Standard 0 5
Bachelor in Mathematics Standard 1 5