Linear algebra [SMATB101]

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 adn 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 eand 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.