Algèbre linéaire

First Quarter:
Fields. Vector spaces and subspaces. Free part, generating set, basis, and dimension. Linear map. Matrix of a linear map. Change of basis and coordinate transformation. Direct sum and direct product. Kernel and image. Affine geometry. Dual space.

Second Quarter:
Determinants. Eigenvectors and diagonalization. Scalar and Hermitian products. Isometries. Symmetric and Hermitian matrices. Quadratic forms. Conics and quadric surfaces
Objectives (and/or specific learning outcomes)

The main objective is to meet the priority needs of subsequent courses in mathematics and physics in the field of linear algebra. Upon completion of this course unit, a student will be able to master the basic concepts and methods of linear algebra.

Courses requiring this course

Lectures, exercise sessions.

References, bibliography, and recommended reading

Lecture notes, available electronically on the Université Virtuelle and in print at the PUB.

Course notes

• Syllabus
• Université virtuelle

Contacts

Samuel FIORINI <Samuel.Fiorini@ulb.be>, Geoffrey JANSSENS <Geoffrey.Janssens@ulb.be>, Joost VERCRUYSSE <Joost.Vercruysse@ulb.be>

Campus

Plaine

Method(s) of evaluation

• written examination

written examination

Written exams in January and June, covering theory and exercises. The January exam covers the material from Q1, and the June exam covers the material from Q2. An optional make-up exam is held in June and covers the material from Q1.

For students who did not pass the course at the end of the June session, a written exam is held for each section in August/September. Registration is required.

The course coordinator reserves the right to invite any student to an additional oral examination in order to verify their personal mastery of the content of the submitted examination, particularly when inconsistencies identified in the examination prevent the course coordinator from properly assessing the student's level of mastery of the knowledge and skills targeted by the course.

Mark calculation method (including weighting of intermediary marks)

The final grade is the arithmetic mean of the Q1 and Q2 grades, unless one of these grades is below 7/20. In that case, the final grade is capped at 7/20.

A partial grade of 10/20 or higher is automatically carried over from one exam period to the next within the same academic year, and may be carried over from one academic year to the next upon written request to the instructors.

Language(s) of evaluation

• french