Mathematics : linear algebra

In the linear algebra part of general mathematics of the first year we will address the following topics:

• real matrices (matrix sum and product, trace, transpose, particular matrices, elementary matrices, invertibility of square matrices, rank of a matrix)
• linear systems (matrix form, Cramer systems, arbitrary systems)
• determinants (properties, link between determinant and invertibility of a matrix, calculation of the inverse by determinant)
• vector spaces (vector subspace, linear dependence and independence, bases, change of base, linear transformations, vectors and eigenvalues, symmetric bilinear forms, dot product, quadratic forms)
• complex numbers (addition and multiplication, de Moivre formula, roots of polynomials, n-th roots)
• Differential equations (only for INGE)

At the end of the teaching unit, students will be able to apply the basic mathematical tools used in economics and econometrics courses.

This part: fundamental notions of linear algebra.

The main objective of this course is the acquisition of quantitative skills. (See contribution to the teaching profile)

Courses requiring this course

Theory: ex cathedra lectures for the whole group

Exercises: subdivision of students into smaller groups

References, bibliography, and recommended reading

The provided slides and selected material will be based on Mathematics for Economists by Carl Simon and Lawrence Bloom.

Course notes

• Université virtuelle

Contacts

Bram De Rock (bram.de.rock@ulb.be)

Campus

Solbosch

Method(s) of evaluation

• written examination

written examination

The course coordinator reserves the right to invite any student to an additional oral interview to verify their personal mastery of the submitted exam content, particularly when inconsistencies found in the exam prevent the coordinator from correctly assessing the level of mastery of the knowledge and skills targeted by the course.

Language(s) of evaluation

• english