Learning outcomes

The algebra course has two main objectives: first to introduce  the bases of linear algebra and matrix computations which are necessary for their subsequent curriculum as mathematician or physicists, and second to train them in the rigourous expression of intuitive and abstract concepts.

Goals

To be able to understand, explain, and illustrate a rigorous proof of linear algebra. 

Content

The course contains elements of linear and multilinear algebra. The framework is that of finite dimensional vector spaces and introduces the notions of linear independence, dual vectors space, matrix computations, eigen structure, metric, inner product. It covers unitary and Hermitian operators and projections. These concepts are applied to the ractical solution of systems of linear equations (Gauss, LU, QR and least-squares).

Table of contents

1.Linear forms and dual spaces  2. .Multilinearity and determinants   3. Metric spaces and untary linear applications 4. Hermitian forms  5. Matricial norms 6. . Projections  

Exercices

The exercices are given in parallel with the course : they aim to explaining, illustratring and precising the course. 

Assessment method

The exam is oral, in two parts : a) a large topic, prepared 20 minutes, with notes and syllabus, including a complete proof b) a list of small questions to be answered  without preparation, on the whole matter. 

Sources, references and any support material

Syllabus 

Language of instruction

French
Training Study programme Block Credits Mandatory
Bachelier en sciences mathématiques Standard 0 5
Bachelier en sciences mathématiques Standard 1 5