Course 2024-2025

Linear algebra [SMATB101]

  • 5 credits
  • 30h+32h
  • 1st quarter
Language of instruction: French / Français

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.

Objectives

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

 

Exercises description

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


Teaching methods

Ex cathedra teaching and exercices. Group project.

Evaluations

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.

Recommended readings

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

Language of instruction

French / Français

Location for course

NAMUR

Organizer

Faculté des sciences
Rue de Bruxelles, 61
5000 NAMUR

Degree of Reference

Undergraduate Degree