Study programme 2020-2021 | 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 Covid-19 assessment methods are possibly planned for the end of Q3 |
---|
Code | Type | Head of UE | Department’s contact details | Teacher(s) |
---|---|---|---|---|
US-B2-SCMATH-003-M | 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 |
---|---|---|---|---|---|---|---|---|
S-MATH-008 | 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, 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
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 |
---|---|
S-MATH-008 |
|
Mode of delivery
AA | Mode of delivery |
---|---|
S-MATH-008 |
|
Required Reading
AA | |
---|---|
S-MATH-008 |
Required Learning Resources/Tools
AA | Required Learning Resources/Tools |
---|---|
S-MATH-008 | Not applicable |
Recommended Reading
AA | |
---|---|
S-MATH-008 |
Recommended Learning Resources/Tools
AA | Recommended Learning Resources/Tools |
---|---|
S-MATH-008 | S. Lang, Linear Algebra, Addison-Wesley R. Mansuy & R. Mneimné, Algèbre linéaire : Réduction des endomorphismes, Vuibert. |
Other Recommended Reading
AA | Other Recommended Reading |
---|---|
S-MATH-008 | Not applicable |
Grade Deferrals of AAs from one year to the next
AA | Grade Deferrals of AAs from one year to the next |
---|---|
S-MATH-008 | Authorized |