COURSE INFORMATION PACKAGE · MAT262
Linear Algebra II
Compulsory · French Open to Erasmus+ exchange students
Content
Objective
Get to grips with basis Linear Algebra.
Course Content
Reminder: Determinant, Dual basis, Dual space, Eigenvalues, Eigenvectors, subspace, eigenspace and diagonalization. Inner product spaces, orthogonality, orthogonal complement. Operators on Inner product spaces, adjoint, self-adjoint, normal operators. Spectral theorem.
Course Learning Outcomes
To understand the structure of linear operators. To be able to recognize diagonalizable and triangulated linear operators or matrices. To understand operators on inner product space and application of spectral theorem.
Teaching and Learning Methods
Lecture and exercises.
References
Linear Algebra Right Done, S. Axler
Algebre Linéaire, Joseph Grifone,
Algèbre linéaire et bilinéaire, F. Cottet Emard, de Boeck, 2007.
Weekly Contents
| Week | Weekly Contents |
|---|---|
| 1 | Introduction of course. Recall: Determinant, Dual Spaces, Dual basis |
| 2 | Eigenvalues, Eigenvecteurs |
| 3 | Diagonalisation |
| 4 | Quiz- Inner product spaces, Norms |
| 5 | Orthogonality |
| 6 | Orthonormal Basis |
| 7 | Orthogonal Complement |
| 8 | Midterm Exam- Adjoint-Self Adjoint Operators |
| 9 | Normal Operators |
| 10 | Spectral Theorem |
| 11 | Midterm Quiz-Positive Operators |
| 12 | Isometries |
| 13 | Unitary operators |
| 14 | Factorizations |
| Week | Weekly Contents |
|---|---|
| 1 | Exercices |
| 2 | Exercices |
| 3 | Exercices |
| 4 | Exercices |
| 5 | Exercices |
| 6 | Exercices |
| 7 | Exercices |
| 8 | Exam |
| 9 | Exercices |
| 10 | Exercices |
| 11 | Exercices |
| 12 | Exercices |
| 13 | Exercices |
| 14 | Exercices |
Assessment System
| Activities | Number | Contribution |
|---|---|---|
| Contribution of in-term studies to overall grade | 2 | 55 |
| Contribution of final exam to overall grade | 1 | 45 |
| Total | 3 | 100 |
| Activities | Number | Contribution |
|---|---|---|
| Assignments | 0 | 0 |
| Presentation | 0 | 0 |
| Midterm Examinations (including preparation) | 1 | 35 |
| Project | 0 | 0 |
| Laboratory | 0 | 0 |
| Other Applications | 0 | 0 |
| Quiz | 2 | 10 |
| Term Paper/ Project | 0 | 0 |
| Portfolio Study | 0 | 0 |
| Reports | 0 | 0 |
| Learning Diary | 0 | 0 |
| Thesis/ Project | 0 | 0 |
| Seminar | 0 | 0 |
| Other | 1 | 45 |
| Make-up | 0 | 0 |
| Total | 4 | 90 |
Relation of Proficiency
| No | Program Learning Outcomes | Contribution | ||||
|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | ||
| 1 | understands principles of deductive reasoning; has experience to verify well-foundedness and exactness of mathematical statements in systematic ways; | X | ||||
| 2 | can properly state and use concepts and results of major mathematical interest; | X | ||||
| 3 | masters current computational techniques and algorithms; has a good ability in their use; can identify relevant tools, among those one has learned, suitable to solve a problem and is able to judge whether or not one is in possession of these tools; | X | ||||
| 4 | is able to express one’s mathematical ideas in an organised way both in written and oral forms; | X | ||||
| 5 | understands relations connecting substantial concepts and results; can switch from one viewpoint to another on mathematical objects (pictures, formulae, precise statements, heuristic trials, list of examples,...); | X | ||||
| 6 | has followed individually a guided learning strategy; has pursued steps toward the resolution of unfamiliar problems; | X | ||||
| 7 | has a theoretical and practical knowledge in computer science well adapted for learning a programming language; | X | ||||
| 8 | has investigated the relevance of modeling and using mathematical tools in natural sciences and in the professional life; is conscious about historical development of mathematical notions; | X | ||||
| 9 | has followed introduction to some mathematical or non-mathematical disciplines after one’s proper choice; had experience to learn selected subjects according to one’s proper arrangement; | X | ||||
| 10 | masters French language as well as other foreign languages, to a level sufficient to study or work abroad. | X | ||||
ECTS
| Activities | Number | Period | Total Workload |
|---|---|---|---|
| Class Hours | 14 | 5 | 70 |
| Working Hours out of Class | 14 | 5 | 70 |
| Assignments | 11 | 2 | 22 |
| Presentation | 2 | 2 | 4 |
| Midterm Examinations (including preparation) | 3 | 7 | 21 |
| Project | 0 | 0 | 0 |
| Laboratory | 0 | 0 | 0 |
| Other Applications | 0 | 0 | 0 |
| Final Examinations (including preparation) | 1 | 15 | 15 |
| Quiz | 0 | 0 | 0 |
| Term Paper/ Project | 0 | 0 | 0 |
| Portfolio Study | 0 | 0 | 0 |
| Reports | 0 | 0 | 0 |
| Learning Diary | 0 | 0 | 0 |
| Thesis/ Project | 0 | 0 | 0 |
| Seminar | 0 | 0 | 0 |
| Other | 0 | 0 | 0 |
| Make-up | 0 | 0 | 0 |
| Yıl Sonu | 0 | 0 | 0 |
| Hazırlık Yıl Sonu | 0 | 0 | 0 |
| Hazırlık Bütünleme | 0 | 0 | 0 |
| Total Workload | 202 | ||
| Total Workload / 25 | 8.08 | ||
| Credits ECTS | 8 | ||