ECUE Matrix algebra for econometrics

Code de l'ECUE : IMEX212

Ce cours appartient à UE Matrix algebra for econometrics (3 ECTS) qui contient 1 ECUE

Structure

EUR ELMI

Domaine disciplinaire

Sciences de gestion et du management

Lieu d'enseignement

Campus Saint Jean d'Angély

Niveau du cours

Master 1

Semestre

Semestre pair , Semestre impair

Langue

Anglais

PRESENTATION

The aim of this course is to extend students' knowledge on the basic and more advanced topics of linear algebra commonly utilized in econometrics.

Nowadays, a solid understanding of vectors, matrices, and their properties is becoming increasingly important in order to conduct modern econometric analysis.

Topics covered in this course will include, among other things, the resolution of linear systems, linear mappings, eigendecomposition of a matrix, dot products, scalar projections, and normed vector spaces.

Particular attention will be devoted to proofs in the resolution of theorems and propositions.

Responsable(s) du cours

Présentiel

18h de cours magistral

PREREQUIS

Avant le début du cours, je dois ...

A preliminary knowledge of the basic notions of real analysis and calculus is required.

OBJECTIFS

A la fin de ce cours, je devrais être capable de...

At the end of the course, students should be able, among other things, to: solve linear systems, perform linear mappings, eigendecompose a matrix, derive dot and cross products.

CONTENU

1. Vector spaces

Algebraic structures, commutative groups, vectors, systems of generators, linear independence, bases, vector subspaces.
2. Matrices

Operations with matrices, Kronecker product, Hadamard product, linear systems, echelon forms, rank and trace of a matrix.
3. Linear transformations

Linear maps, image and kernel of a linear transformation, transformation matrix, transition matrix, matrix similarity.
4. Determinant

Definitions, first minors and cofactors, invertible matrix theorem.
5. Eigenvalues and eigenvectors

Definitions, eigenspaces, characteristic equation, algebraic and geometric multiplicities, eigendecomposition.
6. Euclidean spaces

Dot product, normed vector spaces, normalization, orthogonality, orthogonal complements, Rayleigh quotient.

Accéder au Syllabus complet (Authentification requise)

Important

Ce syllabus n’a aucune valeur contractuelle. Son contenu est susceptible d’évoluer en cours d’année : soyez attentifs aux dernières modifications.