Study programme 20202021  Français  
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 Covid19 assessment methods are possibly planned for the end of Q3 

Code  Type  Head of UE  Department’s contact details  Teacher(s) 

USB2SCMATH003M  Compulsory UE  VOLKOV Maja  S843  Géométrie algébrique 

Language of instruction  Language of assessment  HT(*)  HTPE(*)  HTPS(*)  HR(*)  HD(*)  Credits  Weighting  Term 

 Français  30  15  0  0  0  4  4.00  1st term 
AA Code  Teaching Activity (AA)  HT(*)  HTPE(*)  HTPS(*)  HR(*)  HD(*)  Term  Weighting 

SMATH008  Linear Algebra and Geometry II  30  15  0  0  0  Q1  100.00% 
Programme component 

Objectives of Programme's Learning Outcomes
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, CayleyHamilton theorem, JordanChevalley decomposition.
Duality, bilinear symmetric form, orthogonality, nondegeneracy, transpose and adjoint endomorphism, automorphism, orthogonal basis, definite form.
Euclidean space, norm, orthonormal basis, GramSchmidt process, spectral theorem.
Prior Experience
"Algèbre linéaire et géométrie I" course.
Type of Assessment for UE in Q1
Q1 UE Assessment Comments
Not applicable
Type of Assessment for UE in Q3
Q3 UE Assessment Comments
Not applicable
Type of Resit Assessment for UE in Q1 (BAB1)
Q1 UE Resit Assessment Comments (BAB1)
Not applicable
Type of Teaching Activity/Activities
AA  Type of Teaching Activity/Activities 

SMATH008 

Mode of delivery
AA  Mode of delivery 

SMATH008 

Required Reading
AA  

SMATH008 
Required Learning Resources/Tools
AA  Required Learning Resources/Tools 

SMATH008  Not applicable 
Recommended Reading
AA  

SMATH008 
Recommended Learning Resources/Tools
AA  Recommended Learning Resources/Tools 

SMATH008  S. Lang, Linear Algebra, AddisonWesley R. Mansuy & R. Mneimné, Algèbre linéaire : Réduction des endomorphismes, Vuibert. 
Other Recommended Reading
AA  Other Recommended Reading 

SMATH008  Not applicable 
Grade Deferrals of AAs from one year to the next
AA  Grade Deferrals of AAs from one year to the next 

SMATH008  Authorized 