Linear Algebra

6 ECTS credits
165 h study time

Offer 1 with catalog number 1008038ANR for all students in the 1st semester at a (A) Bachelor - preliminary level.

Semester

1st semester

Enrollment based on exam contract

Impossible

Grading method

Grading (scale from 0 to 20)

Can retake in second session

Yes

Taught in

Dutch

Faculty

Faculteit Ingenieurswetenschappen

Department

Mathematics-TW

Educational team

Philippe Cara (course titular)

Activities and contact hours

36 contact hours Lecture
28 contact hours Seminar, Exercises or Practicals
15 contact hours Independent or External Form of Study

Course Content

- Vector spaces, subspaces, basis, dimension.

- Linear maps, matrix representation, change of basis, dual space, transpose, affine transformations.

- Permutations, multilinear forms, oriented volumes, determinant, systems of linear equations, eigenvectors and eigenvalues.

- Euclidean space, orthogonality, orthonormal basis, orthogonal transformations, isometries, symmetric operators.

- Quadratic forms and quadrics.

- Prehilbertspaces, hermitian operators and unitar linear maps.

Course material

Course text (Required) : Lineaire algebra : stelsels, matrices en afbeeldingen, Volume I, P. Cara, VUB, 2220170009407, 2022
Course text (Required) : Lineaire algebra : stelsels, matrices en afbeeldingen, Volume II, P. Cara, VUB, 2220170009414, 2022

Additional info

P. Cara, Lineaire algebra : stelsels, matrices en afbeeldingen, VUB uitgaven, (2 volumes).

Learning Outcomes

General competencies

The aim of this basic course is to make students familiar with some of the concepts and techniques of linear algebra and analytic geometry. The students have to master not only the fundamental tools of the linear algebra, but also the computational techniques. During class the more fudamental aspects are discussed, and during the problem sessions we practice computational skills and apply them to problems.
The students should understand the introduced concepts, and be able to handle and apply them. A linear algebra course may not degenerate in a mindless application of rules and tricks. For that reason a complete proof is given for nearly all theorems.

Grading

The final grade is composed based on the following categories:
Written Exam determines 100% of the final mark.

Within the Written Exam category, the following assignments need to be completed:

written exam with a relative weight of 1 which comprises 100% of the final mark.

Note: Written exam on theory (50%) and exercises (50%).

Additional info regarding evaluation

The students have to understand the theory and should be able to explain it in a mathematically correct way.

They have to be able to solve simple geometric and algebraic problems.

FIRST SESSION
After the first semester (january):
-Written exam about exercises (closed book) (50%).
-Written exam about theory (50%).

Students who fail in first session but obtain 60% or more for one of the two parts of the exam can opt to transfer that mark to the second session.

SECOND SESSION
- Written exam about exercises (closed book) (50%).
- Written exam about theory (50%)

Allowed unsatisfactory mark

The supplementary Teaching and Examination Regulations of your faculty stipulate whether an allowed unsatisfactory mark for this programme unit is permitted.

Academic context