Algèbre Linéaire (Partie 3)

30 h
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  • 5 Sequences
  • Introductive Level

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Course details


A la fin du cours, l'étudiant sera capable

  • de définir les concepts théoriques introduits en cours et d'en donner des exemples illustratifs ;
  • de reconnaître un produit scalaire et maîtriser les propriétés associées à un tel objet (e.g. Inégalité de Cauchy-Schwarz, inégalité du triangle) ;
  • de et maîtriser les notions de bases liées à l'orthogonalité (e.g. familles/bases orthogonales, familles/bases orthonormales, orthogonal d'un sous-espace, Théorème de Pythagore) ;
  • de construire une base orthonormée d'un sous-espace vectoriel d'un espace euclidien à l'aide du procédé de Gram-Schmidt ;
  • de calculer la meilleure approximation quadratique d'un vecteur ;
  • de calculer la solution au sens des moindres carrés d'un système linéaire ;
  • de calculer la factorisation QR d'une matrice donnée, lorsque cela est possible ;
  • de diagonaliser orthogonalement une matrice symétrique donnée ;
  • de déterminer les axes principaux d'une forme quadratique donnée ;
  • de calculer la décomposition en valeurs singulières d'une matrice donnée.


Baccalauréat/maturité fédérale, maîtrise de l'algèbre enseignée au lycée/gymnase, bonne connaissance de la matière enseignée dans les MOOCs

et .


Donna Testerman

Claude Marion

Mikaël Cavallin


The École polytechnique fédérale de Lausanne (EPFL, English: Swiss Federal Institute of Technology in Lausanne) is a research university in Lausanne, Switzerland, that specialises in physical sciences and engineering.

One of the two Swiss Federal Institutes of Technology, the school was founded by the Swiss Federal Government with the stated mission to:

Educate engineers and scientists to the highest international standing
Be a national center of excellence in science and technology
Provide a hub for interaction between the scientific community and the industry
EPFL is considered one of the most prestigious universities in the world for engineering and sciences, ranking 17th overall and 10th in engineering in the 2015 QS World University Rankings; 34th overall and 12th in engineering in the 2015 Times Higher Education World University Rankings.


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