ECTS - Matrix Analysis
Matrix Analysis (MATH333) Course Detail
| Course Name | Course Code | Season | Lecture Hours | Application Hours | Lab Hours | Credit | ECTS |
|---|---|---|---|---|---|---|---|
| Matrix Analysis | MATH333 | Elective Courses | 3 | 0 | 0 | 3 | 6 |
| Pre-requisite Course(s) |
|---|
| (MATH231 veya MATH275) |
| Course Language | English |
|---|---|
| Course Type | Elective Courses |
| Course Level | Bachelor’s Degree (First Cycle) |
| 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 | |
|---|---|
| Major Area Courses | X |
| 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 | Acquires skills to use the advanced theoretical and applied knowledge obtained at the mathematics bachelors program to do further academic and scientific research in both mathematics-based graduate programs and public or private sectors. | X | ||||
| 2 | Transplants and applies the theoretical and applicable knowledge gained in their field to the secondary education by using suitable tools and devices. | X | ||||
| 3 | Acquires the skill of choosing, using and improving problem solving techniques which are needed for modeling and solving current problems in mathematics or related fields by using the obtained knowledge and skills. | X | ||||
| 4 | Acquires analytical thinking and uses time effectively in the process of deduction | X | ||||
| 5 | Acquires basic software knowledge necessary to work in the computer science related fields and together with the skills to use information technologies effectively. | X | ||||
| 6 | Obtains the ability to collect data, to analyze, interpret and use statistical methods necessary in decision making processes. | X | ||||
| 7 | Acquires the level of knowledge to be able to work in the mathematics and related fields and keeps professional knowledge and skills up-to-date with awareness in the importance of lifelong learning. | X | ||||
| 8 | Takes responsibility in mathematics related areas and has the ability to work affectively either individually or as a member of a team. | 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 the ability to communicate ideas with peers supported by qualitative and quantitative data. | X | ||||
| 11 | Has professional and 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 | ||