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.
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.
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.
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
The exercices are given in parallel with the course and are supervised by a teaching assistant.
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.
Two manuscripts (lecture notes and book of exercices) are available.