ECTS - Matrix Analysis
Matrix Analysis (MATH333) Course Detail
| Course Name | Course Code | Season | Lecture Hours | Application Hours | Lab Hours | Credit | ECTS |
|---|---|---|---|---|---|---|---|
| Matrix Analysis | MATH333 | Area Elective | 3 | 0 | 0 | 3 | 6 |
| Pre-requisite Course(s) |
|---|
| (MATH231 veya MATH275) |
| Course Language | English |
|---|---|
| Course Type | Elective Courses |
| Course Level | Natural & Applied Sciences Master's Degree |
| Mode of Delivery | Face To Face |
| Learning and Teaching Strategies | Lecture, Question and Answer, Drill and Practice. |
| Course Lecturer(s) |
|
| Course Objectives | Linear algebra and matrix theory have been fundamental tools in mathematical disciplines. Having the basic knowlegde and properties of linear transformations, vector spaces, vectors and matrices the aim is to present classical and recent results of matrix analysis that have proved to be important to applied mathematics. |
| Course Learning Outcomes |
The students who succeeded in this course;
|
| Course Content | Preliminaries, eigenvalues, eigenvectors and similarity, unitary equivalence and normal matrices, Canonical forms, Hermitian and symmetric matrices, norms for vectors and matrices, location and perturbation of eigenvalues, positive definite matrices, nonnegative matrices. |
Weekly Subjects and Releated Preparation Studies
| Week | Subjects | Preparation |
|---|---|---|
| 1 | Vector Spaces, Matrices, Determinants, Rank, Nonsingularity, The Usual Inner Product, Partitioned Matrices | pp. 1-18 |
| 2 | The Eigenvalue-Eigenvector Equation, The Characteristic Polynomial, Similarity | pp. 33-57 |
| 3 | Unitary Matrices, Unitary Equivalence | pp. 65-78 |
| 4 | Schur’s Unitary Triangularization Theorem, Normal Matrices | pp. 79-111 |
| 5 | The Jordan Canonical Form, Polynomials and Matrices, The Minimal Polynomial | pp. 119-149 |
| 6 | Triangular Factorization, LU Decomposition | pp. 158-166 |
| 7 | Hermitian Matrices, Properties and Characterizations of Hermitian Matrices, Complex Symmetric Matrices | pp. 167-217 |
| 8 | Defining Properties of Vector Norms and Inner Products, Examles of Vector Norms, Algebraic Properties of Vector Norms | pp. 257-268 |
| 9 | Matrix Norms, Vector Norms on Matrices, Errors in Inverses and Solutions of Linear Systems | pp. 290-342 |
| 10 | Gersgorin Discs, Perturbation Theorems, Other Inclusion Regions | pp. 343-390 |
| 11 | Positive Definite Matrices, Their Properties and Characterizations | pp. 391-410 |
| 12 | The Polar Form and The SVD, The Schur Product Form, Simultaneous Diagonalization | pp. 411-468 |
| 13 | Nonnegative Matrices; Inequalities and Generalities, Positive Matrices | pp. 487-502 |
| 14 | Nonnegative Matrices, Irreducible Nonnnegative Matrices | pp. 503-514 |
| 15 | General Review | |
| 16 | Final Exam |
Sources
| Course Book | 1. Matrix Analysis, R.A.Horn & C.R.Johnson, Cambridge University Press, 1991. |
|---|---|
| Other Sources | 2. 1- Matrix Theory; Basic Results and Techniques, By F.Zhang, Springer, 2011 |
| 3. 2- Elementary Linear Algebra, B.Kolman &D.R.Hill, 9th edition, Prentice Hall, 2008. |
Evaluation System
| Requirements | Number | Percentage of Grade |
|---|---|---|
| Attendance/Participation | - | - |
| Laboratory | - | - |
| Application | - | - |
| Field Work | - | - |
| Special Course Internship | - | - |
| Quizzes/Studio Critics | - | - |
| Homework Assignments | 5 | 10 |
| Presentation | - | - |
| Project | - | - |
| Report | - | - |
| Seminar | - | - |
| Midterms Exams/Midterms Jury | 2 | 55 |
| Final Exam/Final Jury | 1 | 35 |
| Toplam | 8 | 100 |
| Percentage of Semester Work | 65 |
|---|---|
| Percentage of Final Work | 35 |
| Total | 100 |
Course Category
| Core Courses | X |
|---|---|
| Major Area Courses | |
| Supportive Courses | |
| Media and Managment Skills Courses | |
| Transferable Skill Courses |
The Relation Between Course Learning Competencies and Program Qualifications
| # | Program Qualifications / Competencies | Level of Contribution | ||||
|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | ||
| 1 | Has the ability to apply scientific knowledge gained in the undergraduate education and to expand and extend knowledge in the same or in a different area. | X | ||||
| 2 | Has the ability to obtain, to evaluate, to interpret and to apply information by doing scientific research. | X | ||||
| 3 | Can apply gained knowledge and problem solving abilities in inter-disciplinary research. | X | ||||
| 4 | Has the ability to work independently within research area, to state the problem, to develop solution techniques, to solve the problem, to evaluate the obtained results and to apply them when necessary. | X | ||||
| 5 | Takes responsibility individually and as a team member to improve systematic approaches to produce solutions in unexpected complicated situations related to the area of study. | X | ||||
| 6 | Can develop strategies, implement plans and principles on the area of study and can evaluate obtained results within the framework. | X | ||||
| 7 | Can develop and extend the knowledge in the area and to use them with scientific, social and ethical responsibility. | X | ||||
| 8 | Has the ability to follow recent developments within the area of research, to support research with scientific arguments and data, to communicate the information on the area of expertise in a systematically by means of written report and oral/visual presentation. | X | ||||
| 9 | Has proficiency in English language and has the ability to communicate with colleagues and to follow the innovations in mathematics and related fields. | X | ||||
| 10 | Has software and hardware knowledge in the area of expertise, and has proficient information and communication technology knowledge. | X | ||||
| 11 | Has professional ethical consciousness and responsibility which takes into account the universal and social dimensions in the process of data collection, interpretation, implementation and declaration of results in mathematics and its applications. | X | ||||
ECTS/Workload Table
| Activities | Number | Duration (Hours) | Total Workload |
|---|---|---|---|
| Course Hours (Including Exam Week: 16 x Total Hours) | |||
| Laboratory | |||
| Application | |||
| Special Course Internship | |||
| Field Work | |||
| Study Hours Out of Class | 16 | 3 | 48 |
| Presentation/Seminar Prepration | |||
| Project | |||
| Report | |||
| Homework Assignments | 5 | 6 | 30 |
| Quizzes/Studio Critics | |||
| Prepration of Midterm Exams/Midterm Jury | 2 | 15 | 30 |
| Prepration of Final Exams/Final Jury | |||
| Total Workload | 108 | ||