Study programme 2020-2021Français
Linear Algebra and Geometry II
Programme component of Bachelor's in Mathematics à la Faculty of Science

Students are asked to consult the ECTS course descriptions for each learning activity (AA) to know what special Covid-19 assessment methods are possibly planned for the end of Q3

CodeTypeHead of UE Department’s
contact details
US-B2-SCMATH-003-MCompulsory UEVOLKOV MajaS843 - Géométrie algébrique
  • VOLKOV Maja

of instruction
of assessment
HT(*) HTPE(*) HTPS(*) HR(*) HD(*) CreditsWeighting Term
  • Français
Français301500044.001st term

AA CodeTeaching Activity (AA) HT(*) HTPE(*) HTPS(*) HR(*) HD(*) Term Weighting
S-MATH-008Linear Algebra and Geometry II3015000Q1100.00%
Programme component

Objectives of Programme's Learning Outcomes

  • Understand "elementary" mathematics profoundly
    • Use vector spaces, linear applications and the techniques associated with them
    • Understand and use the naive set theory
    • Understand basic algebraic structures
    • Manipulate previously acquired knowledge that appears in a question
    • Give examples and counterexamples for definitions, properties, theorems, etc.
  • Understand and produce strict mathematical reasoning
    • Write clearly and concisely
    • Use mathematical vocabulary and formalism appropriately
    • Make sense of formal expressions
    • Rely on a picture to illustrate a concept, rationale, etc.
  • Solve new problems
    • Abstract and manipulate theories and use these to solve problems
    • Adapt an argument to a similar situation
    • Use knowledge from different fields to address issues

Learning Outcomes of UE

Structure results in linear algebra: reduction of endomorphisms and spectral theory in Euclidean spaces.
The aim of this course is to develop the algebraic theory of endomorphism algebras of finite dimensional vector spaces, possibly endowed with a definite symmetric bilinear form.

Content of UE

Diagonalisation, eigenvalue, eigenvector, characteristic polynomial, minimal polynomial, Cayley-Hamilton theorem, Jordan-Chevalley decomposition.
Duality, bilinear symmetric form, orthogonality, non-degeneracy, transpose and adjoint endomorphism, automorphism, orthogonal basis, definite form.
Euclidean space, norm, orthonormal basis, Gram-Schmidt process, spectral theorem.

Prior Experience

"Algèbre linéaire et géométrie I" course. 

Type of Assessment for UE in Q1

  • Written examination

Q1 UE Assessment Comments

Not applicable

Type of Assessment for UE in Q3

  • Written examination

Q3 UE Assessment Comments

Not applicable

Type of Resit Assessment for UE in Q1 (BAB1)

  • N/A

Q1 UE Resit Assessment Comments (BAB1)

Not applicable

Type of Teaching Activity/Activities

AAType of Teaching Activity/Activities
  • Cours magistraux
  • Exercices dirigés

Mode of delivery

AAMode of delivery
  • Face to face

Required Reading


Required Learning Resources/Tools

AARequired Learning Resources/Tools
S-MATH-008Not applicable

Recommended Reading


Recommended Learning Resources/Tools

AARecommended Learning Resources/Tools
S-MATH-008S. Lang, Linear Algebra, Addison-Wesley
R. Mansuy & R. Mneimné, Algèbre linéaire : Réduction des endomorphismes, Vuibert.

Other Recommended Reading

AAOther Recommended Reading
S-MATH-008Not applicable

Grade Deferrals of AAs from one year to the next

AAGrade Deferrals of AAs from one year to the next
(*) HT : Hours of theory - HTPE : Hours of in-class exercices - HTPS : hours of practical work - HD : HMiscellaneous time - HR : Hours of remedial classes. - Per. (Period), Y=Year, Q1=1st term et Q2=2nd term
Date de génération : 09/07/2021
20, place du Parc, B7000 Mons - Belgique
Tél: +32 (0)65 373111