Linear Algebra(ING207)
Course Code | Course Name | Semester | Theory | Practice | Lab | Credit | ECTS |
---|---|---|---|---|---|---|---|
ING207 | Linear Algebra | 3 | 2 | 2 | 0 | 3 | 5 |
Prerequisites | |
Admission Requirements |
Language of Instruction | French |
Course Type | Compulsory |
Course Level | Bachelor Degree |
Course Instructor(s) | Marie Christine PEROUEME mcperoueme@voila.fr (Email) |
Assistant | |
Objective |
Mathematical problems such as solving systems linear differentials (which occur in many areas physics such as mechanics or electronics) or analysis in principal components in statistics use the diagonalization of square matrices. Determine if a matrix is ??diagonalizable, and in this case, diagonalizing it is therefore the key to this course. In this context, the objectives of this course are: • Explain to students how the determinant of a matrix is defined using permutations and their signature, in particular in order to be able to define the characteristic polynomial. • Teach students to determine the specific elements of a matrix. • Demonstrate to the students the conditions of diagonalization of a matrix. • Explain to the students how to use diagonalization to solve linear systems. |
Content |
1. Symmetric group: decomposition into products and signature of a permutation 2. Determinants: definition, properties and calculation rules 3. Determinants: determinants of "small" dimensions, classical determinants 4. Diagonalization: Introduction and first examples 5. Classical determinant applications 6. Diagonalization: criterion of diagonalization (case of multiple eigenvalues) 7. Diagonalization: diagonalization of "small" dimension matrices 8. Partial Examination 9. Diagonalization: calculation of the nth powers of a diagonalizable matrix 10. Polynomials of matrices, canceling polynomials - Cayleigh Hamilton Theorem 11. Application to the calculation of the nth powers of a matrix (diagonalizable or not) 12. Application to linear recurrent sequences 13. Application to differential systems (diagonalizable case) 14. Practical studies |
Course Learning Outcomes |
The student who will take this course will develop the elements of competence following and will be able to: 1. Calculate the decomposition in cycles with disjoint supports and signing a permutation. 2. Calculate the determinant of a square matrix. 3. Determine the characteristic polynomial (and therefore, the eigenvalues) of a matrix. 4. Determine the eigenspaces of a matrix. 5. Illustrate on geometric examples (homothety, rotation, symmetry ...) the dimension and direction of the proper spaces. 6. Prove if a matrix is diagonalizable in R or in C. 7. Determine the diagonalized matrix as well as the associated matrix passage. 8. Solve linear systems (equations differential or recurrent sequences). |
Teaching and Learning Methods | Lectures and supervised works/tutorials |
References |
1. Lectures notes ans worksheets 2. http://braise.univ-rennes1.fr/braise.cgi 3. http://www.unisciel.fr |
Theory Topics
Week | Weekly Contents |
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Practice Topics
Week | Weekly Contents |
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Contribution to Overall Grade
Number | Contribution | |
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Toplam | 0 | 0 |
In-Term Studies
Number | Contribution | |
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Toplam | 0 | 0 |
No | Program Learning Outcomes | Contribution | ||||
---|---|---|---|---|---|---|
1 | 2 | 3 | 4 | 5 |
Activities | Number | Period | Total Workload |
---|---|---|---|
Total Workload | 0 | ||
Total Workload / 25 | 0,00 | ||
Credits ECTS | 0 |