Euclidean space (04_XEEUC)
- Coefficient : 2
- Hourly Volume: 50h (including 27h supervised)
- CTD : 27h supervised (and 4.5h unsupervised)
- Out-of-schedule personal work : 18.5h
- Including project : 27h supervised and 23h unsupervised project
AATs Lists
Description
Through an approach based on problems and projects (analysis of a DTMF signal, image compression, etc.), students will become familiar with the classic notions at play, in various spaces (functional spaces, spaces of matrices...) - Scalar product and associated norm - Orthonormal basis of a Euclidean space (Gramm-Schmidt process) - Orthogonal projection - Solution approximation
In addition, students will have to implement the methods in Python as part of group projects and make oral presentations of these projects.
Learning Outcomes AAv (AAv)
AAv1 [heures: 25, B2,B3] : At the end of the teaching, each student knows how to implement the relevant mathematical tools to define and calculate an orthogonal projection on a finite orthonormal family, in order to solve problems of approximation, in any type of vector space provided with a scalar product.
AAv2 [heures: 25, B2,B3] : At the end of the teaching, each student knows how to implement the relevant mathematical tools to construct an orthonormal basis from a finite family of vectors, in a vector space provided of a scalar product.
Assessment methods
- Evaluation of the progress of projects throughout the semester, via rapporteurs who change, for each group, from session to session.
- Oral presentations which summarize the projects, the methods used, their mathematical justifications and the results obtained.
- A common test for all groups
Key Words
Euclidean spaces
Prerequisites
S2 algebra: Vector spaces, matrix calculation, linear applications