ECUE Matrix algebra for econometrics

ECUE's code : IMEX212

This course belong to UE Matrix algebra for econometrics (3 ECTS) which contains 1 ECUE

Structure

EUR ELMI

Disciplinary domain

Sciences de gestion et du management

Campus

Campus Saint Jean d'Angély

Course's level

Master 1

Semester

Semestre pair , Semestre impair

Language

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.

Course's manager(s)

In class

18h of lectures

PREREQUISITES

Before the start of the course, I must ...

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

OBJECTIVES

By the end of this course, I should be able to...

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.

CONTENT

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.

Access to complete Syllabus (Authentification required)

Important

This syllabus has no contractual value. Its content is subject to change throughout this year: be aware to the last updates