Teacher(s)
Delvenne JeanCharles (compensates Jungers Raphaël); Jungers Raphaël;
Language
English
> Frenchfriendly
> Frenchfriendly
Prerequisites
Basic knowledge (1st cycle) in linear algebra and numerical analysis.
Main themes
The course builds on the solid mathematical foundations of Matrix theory in order to elaborate algorithmic solutions to major challenges involving computations with/on matrices.
 Matrices defined over a field/ring/nonnegative: applications and challenges
 Canonical forms, decompositions, eigen and singular values
 Norms, convexity, structured matrices: sparse/adjacency matrices
 Recent computational challenges: Nonnegative Matrix Factorization, matrix semigroups
Learning outcomes
At the end of this learning unit, the student is able to :  
1 
Contribution of the course to the program objectives :

Content
After an introduction recalling some basic notions, we discuss the following topics:
 Complements on determinants
 The singular value decomposition and its applications. Angles between subspaces, generalized inverses, projectors, leastsquares problems
 Eigenvalue decomposition: Schur and Jordan form
 Approximations and variational characterization of eigenvalues
 Congruence and stability: inertia, Lyapunov equation, stability analysis of dynamical systems
 Structured and Polynomial matrices: Euclid algorithm, Smith normal form, fast algorithms.
 Nonnegative matrices: PerronFrobenius theorem, stochastic matrices
 Matrix semigroups: algebraic structure, algorithms and applications (NMF, Joint Spectral Characteristics)
Teaching methods
 Regular classes with a schedule fixed by the EPL.
 A seminar with presentations by the students is organized at the end of the quadrimester.
 Exercises or homeworks made individually or in small groups, with the possibility to consult teaching assistants..
 Details announced during the first class.
Evaluation methods
The evaluation of the students is partly based on a written (or oral, depending of the circumstances) exam organized according to the rules imposed by the EPL. The exam material corresponds to the contents of the lectures and lecture notes, with the possible exception of certain parts specified after the last session of the course. The exam represents 14/20 of the final grade.
For a written exam, in case of doubt, the teacher might invite the student for a supplementary oral exam.
The other part of the evaluation is based on the assignments and presentations made during the semester. It amounts to 6/20 of the final grade, in Jan and unchanged in Sept.
For a written exam, in case of doubt, the teacher might invite the student for a supplementary oral exam.
The other part of the evaluation is based on the assignments and presentations made during the semester. It amounts to 6/20 of the final grade, in Jan and unchanged in Sept.
Online resources
Bibliography
Le support de cours se compose d'ouvrages de référence, de notes de cours détaillées et de documents complémentaires disponibles sur Moodle.
Ouvrages de référence :
Ouvrages de référence :
 G.H. Golub and C.F. Van Loan (1989). Matrix Computations, 2nd Ed, Johns Hopkins University Press, Baltimore.
 P. Lancaster and M. Tismenetsky (1985). The Theory of Matrices, 2nd Ed, Academic Press, New York
Teaching materials
 LINMA 2380 Course notes by R.J. et al.
Faculty or entity
Programmes / formations proposant cette unité d'enseignement (UE)
Title of the programme
Sigle
Credits
Prerequisites
Learning outcomes
Master [120] in Mathematics
Master [120] in Electrical Engineering
Master [120] in Mathematical Engineering
Master [120] in Data Science Engineering
Master [120] in Data Science: Information Technology