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Information
| Code | IEM1829 |
| Name | Matrix Theory |
| Term | 2024-2025 Academic Year |
| Term | Fall and Spring |
| Duration (T+A) | 4-0 (T-A) (17 Week) |
| ECTS | 8 ECTS |
| National Credit | 4 National Credit |
| Teaching Language | Türkçe |
| Level | Doktora Dersi |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Doç. Dr. ERSİN KIRAL |
| Course Instructor |
1 |
Course Goal / Objective
The aim is to develop an understanding of linear equations and matrices while gaining the ability to solve linear systems. Comprehending the relationship between matrices and linear transformations through determinants and real vector spaces is targeted. Analyzing eigenvalues and eigenvectors and applying linear algebra concepts across various disciplines are intended.
Course Content
The course content covers linear equations and matrices, examining solution methods for linear systems. The concept and properties of determinants are explored, with a focus on the fundamental concepts of real vector spaces. The relationship between linear transformations and matrices is analyzed, explaining the mathematical foundations of these transformations. The concepts of eigenvalues and eigenvectors are studied, analyzing their impact on matrices and linear systems.
Course Precondition
No prerequisites
Resources
Kolman, B., Hill, D. R., & Akın, Ö. (2002). Uygulamalı lineer cebir. Palme Yayıncılık.
Notes
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Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Explain algebraic operations between matrices and matrices |
| LO02 | Classifies matrices according to their different properties |
| LO03 | Develops different solutions to mathematical models using algebraic properties of matrices |
| LO04 | Displays a mathematical model in matrix form |
| LO05 | Performs matrix operations with a computer program |
| LO06 | Evaluates the concept of determinants and their properties to explain the fundamental concepts of real vector spaces. |
| LO07 | Uses the concepts of eigenvalues and eigenvectors to analyze their effects on matrices and linear systems. |
| LO08 | Analyzes solution methods for linear systems using linear equations and matrices. |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Identify an econometric problem and propose a new solution to it | |
| PLO02 | Bilgi - Kuramsal, Olgusal | Develops new knowledge using current concepts in Econometrics, Statistics and Operations Research | 3 |
| PLO03 | Bilgi - Kuramsal, Olgusal | Explain for what purpose and how econometric methods are applied to other fields and disciplines | 1 |
| PLO04 | Beceriler - Bilişsel, Uygulamalı | Using her knowledge, brings original solutions to problems in Economics, Business Administration and other social sciences | |
| PLO05 | Beceriler - Bilişsel, Uygulamalı | Creates a new model using mathematics, statistics and econometrics knowledge to solve the problem encountered | 5 |
| PLO06 | Beceriler - Bilişsel, Uygulamalı | Interprets the results obtained from the most appropriate method to predict the model | 1 |
| PLO07 | Beceriler - Bilişsel, Uygulamalı | Performs conceptual analysis to develop solutions to problems | |
| PLO08 | Beceriler - Bilişsel, Uygulamalı | Collects data on purpose | |
| PLO09 | Beceriler - Bilişsel, Uygulamalı | Synthesizes the information obtained by using different sources within the framework of academic rules in a field of research | |
| PLO10 | Beceriler - Bilişsel, Uygulamalı | Presents analysis results conveniently | 2 |
| PLO11 | Beceriler - Bilişsel, Uygulamalı | Converts its findings into a master's thesis or a professional report in Turkish or a foreign language | 3 |
| PLO12 | Beceriler - Bilişsel, Uygulamalı | It researches current approaches and methods to solve the problems it encounters and proposes new solutions | 4 |
| PLO13 | Beceriler - Bilişsel, Uygulamalı | Develops long-term plans and strategies using econometric and statistical methods | |
| PLO14 | Beceriler - Bilişsel, Uygulamalı | Uses a package program/writes a new code for Econometrics, Statistics, and Operation Research | |
| PLO15 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Performs self-study using knowledge of Econometrics, Statistics and Operations to solve a problem | 3 |
| PLO16 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Leads the team by taking responsibility | |
| PLO17 | Yetkinlikler - Öğrenme Yetkinliği | Being aware of the necessity of lifelong learning, it constantly renews itself by following the current developments in the field of study | |
| PLO18 | Yetkinlikler - İletişim ve Sosyal Yetkinlik | Uses acquired knowledge in the field to determine the vision, aim, and goals for an organization/institution | |
| PLO19 | Yetkinlikler - İletişim ve Sosyal Yetkinlik | Interprets the feelings, thoughts and behaviors of the related persons correctly/expresses himself/herself correctly in written and verbal form | |
| PLO20 | Yetkinlikler - Alana Özgü Yetkinlik | Applies social, scientific and professional ethical values | |
| PLO21 | Yetkinlikler - Alana Özgü Yetkinlik | Interprets data on economic and social events by following current issues |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Notations and definitions ( determinant, rank, trace, qadratic forms, orthogonal martices) | Reading | Öğretim Yöntemleri: Anlatım, Problem Çözme |
| 2 | Similar matrices, Symmetric matrices | Reading | Öğretim Yöntemleri: Anlatım, Problem Çözme |
| 3 | Eigenvectors and eigenvalues | Reading | Öğretim Yöntemleri: Anlatım, Problem Çözme, Alıştırma ve Uygulama |
| 4 | Vector space, vector subspace, basis of a vector space, column and null space of a marrix | Reading | Öğretim Yöntemleri: Anlatım, Problem Çözme |
| 5 | Basic theorems of generalized inverse | Reading | Öğretim Yöntemleri: Anlatım, Problem Çözme |
| 6 | Computing formulas for the g-inverse | Reading | Öğretim Yöntemleri: Anlatım, Problem Çözme |
| 7 | Conditional inverse, Hermite form of matrices | Reading | Öğretim Yöntemleri: Anlatım, Problem Çözme |
| 8 | Mid-Term Exam | Mid-Term Exam | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | solutions to systems of linear equations, | Reading | Öğretim Yöntemleri: Anlatım, Problem Çözme |
| 10 | Approximate solutions to inconsitent systems of linear equations, Least squares | Reading | Öğretim Yöntemleri: Anlatım, Problem Çözme |
| 11 | Pattern matrices | Reading | Öğretim Yöntemleri: Anlatım, Problem Çözme |
| 12 | Trace of matrik and its properties | Reading | Öğretim Yöntemleri: Anlatım, Problem Çözme |
| 13 | Matrix derivatives | Reading | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 14 | nnd matrices and its properties | Reading | Öğretim Yöntemleri: Anlatım, Problem Çözme |
| 15 | pd and nnd matrices and its properties | Reading | Öğretim Yöntemleri: Anlatım, Problem Çözme |
| 16 | Term Exams | Term Exams | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | Term Exams | Ölçme Yöntemleri: Yazılı Sınav |
Student Workload - ECTS
| Works | Number | Time (Hour) | Workload (Hour) |
|---|---|---|---|
| Course Related Works | |||
| Class Time (Exam weeks are excluded) | 14 | 4 | 56 |
| Out of Class Study (Preliminary Work, Practice) | 14 | 8 | 112 |
| Assesment Related Works | |||
| Homeworks, Projects, Others | 2 | 4 | 8 |
| Mid-term Exams (Written, Oral, etc.) | 1 | 12 | 12 |
| Final Exam | 1 | 24 | 24 |
| Total Workload (Hour) | 212 | ||
| Total Workload / 25 (h) | 8,48 | ||
| ECTS | 8 ECTS | ||