- 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
At the end of this learning unit, the student is able to :
Contribution of the course to the program objectives :
- Complements on determinants
- The singular value decomposition and its applications. Angles between subspaces, generalized inverses, projectors, least-squares 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: Perron-Frobenius theorem, stochastic matrices
- Matrix semigroups: algebraic structure, algorithms and applications (NMF, Joint Spectral Characteristics)
Due to the COVID-19 crisis, the information in this section is particularly likely to change.
- 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.
Due to the COVID-19 crisis, the information in this section is particularly likely to change.The evaluation of the students is partly based on an exam organized according to the rules imposed by the EPL. The exam material corresponds to the contents of the course material, with the possible exception of certain parts specified after the last session of the course.
The other part of the evaluation is based on the homeworks and presentations made during the semester.
More elaborate information on the evaluation procedure is given in the course plan, made available at the beginning of the academic year.
For a written exam, in case of doubt, the teacher might invite the student for a supplementary oral exam.
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
- LINMA 2380 Course notes by R.J. et al.