Advanced Linear Algebra
Mathematics
Institute of Natural and Applied Sciences
Second Cycle (Master's Degree)
| Course Unit Title | Course Unit Code | Type of Course Unit | Level of Course Unit | Year of Study | Semester | ECTS Credits |
|---|---|---|---|---|---|---|
| Advanced Linear Algebra | MAT517 | Compulsory | Master's degree | 1 | Spring | 8 |
Name of Lecturer(s)
Prof. Dr. Neşe ÖMÜR
Prof. Dr. Serdal PAMUK
Associate Prof. Dr. Yücel TÜRKER ULUTAŞ
Learning Outcomes of the Course Unit
1) He/She knows the concepts of vector spaces and linear transformations.
2) He/She knows the concepts of characteristic polynomials and eigenvalues, eigenvectors.
3) He/She knows the concepts of LU-factorization, Cholesky factorization, Householder transformation and QR-factorization.
Program Competencies-Learning Outcomes Relation
| Program Competencies | ||||||||
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | ||
| Learning Outcomes | ||||||||
| 1 | No relation | No relation | No relation | No relation | No relation | No relation | No relation | |
| 2 | No relation | No relation | No relation | No relation | No relation | No relation | No relation | |
| 3 | No relation | No relation | No relation | No relation | No relation | No relation | No relation | |
Mode of Delivery
Face to Face
Prerequisites and Co-Requisites
None
Recommended Optional Programme Components
Not Required
Course Contents
Vector spaces, subspaces, Direct sums, spanning sets and linear independence, linear transformation, the kernel and image of a linear transformation, isomorphisms, the isomorphism theorems, Linear functionals and dual spaces, modules, free modules, the structure of a linear operator, the characteristic polynomial, Eigenvalues and eigenvectors, real and complex inner product spaces, structure theory for normal operators, Bessel and Schwartz inequalities, quadratic forms, convexs sets, matrix factorizations, LU-factorization, Cholesky factorization, Householder transformation and QR-factorization.
Weekly Schedule
1) Vector spaces, subspaces2) Direct sums, spanning sets and linear independence
3) linear transformation, the kernel and image of a linear transformation
4) linear transformation, the kernel and image of a linear transformation
5) isomorphisms, the isomorphism theorems,
6) Linear functionals and dual spaces
7) modules, free modules
8) Midterm examination/Assessment
9) the structure of a linear operator
10) the characteristic polynomial, Eigenvalues and eigenvectors
11) real and complex inner product spaces
12) real and complex inner product spaces
13) structure theory for normal operators,Bessel ve Schwartz inequalities
14) quadratic forms, convexs sets
15) matrix factorizations, LU-factorization
16) Final examination
Recommended or Required Reading
1- Steven Roman, Advance Linear Algebra, Third Edition, , 2007.
2- Fuhzen Zhang, Matrix Theory, Basic Results and Techniques, 1999.
3- S. Lang, Linear Algebra, Addison-Wesley 1987
Planned Learning Activities and Teaching Methods
1) Lecture
2) Discussion
3) Demonstration
4) Group Study
5) Problem Solving
Assessment Methods and Criteria
Contribution of Midterm Examination to Course Grade |
20% |
|---|---|
Contribution of Final Examination to Course Grade |
80% |
Total |
100% |
Language of Instruction
Turkish
Work Placement(s)
Not Required