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) |
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(MATH231 veya MATH275) |
Course Language | English |
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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) |
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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;
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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 |
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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. |
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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 |
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Percentage of Final Work | 35 |
Total | 100 |
Course Category
Core Courses | X |
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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 | ||||
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1 | 2 | 3 | 4 | 5 | ||
1 | They acquire the skills to understand, explain, and use the basic concepts and methods of economics. | |||||
2 | Acquires macro-economic analysis skills. | |||||
3 | Acquire microeconomic analysis skills. | |||||
4 | Understands the formulation and implementation of economic policies at local, national, regional and/or global levels. | |||||
5 | Learn different approaches to the economy and economic issues. | |||||
6 | Learn qualitative and quantitative research techniques in economic analysis. | X | ||||
7 | Improving the ability to use modern software, hardware and/or other technological tools. | |||||
8 | Develops intra-disciplinary and inter-disciplinary team work skills. | X | ||||
9 | Contributes to open-mindedness by encouraging critical analysis, discussion, and/or lifelong learning. | |||||
10 | Develops a sense of work ethics and social responsibility. | |||||
11 | Develops communication skills. | |||||
12 | Improving the ability to effectively apply knowledge and skills in at least one of the following areas: Economic policy, public policy, international economic relations, industrial relations, monetary and financial relations | X |
ECTS/Workload Table
Activities | Number | Duration (Hours) | Total Workload |
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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 |