TÜRKÇE
ENGLISH
Information
| Code | IEM713 |
| Name | Matrix Theory |
| Term | 2024-2025 Academic Year |
| Term | Fall and Spring |
| Duration (T+A) | 3-0 (T-A) (17 Week) |
| ECTS | 6 ECTS |
| National Credit | 3 National Credit |
| Teaching Language | Türkçe |
| Level | Yüksek Lisans Dersi |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Doç. Dr. ERSİN KIRAL |
| Course Instructor |
Doç. Dr. ERSİN KIRAL
(A Group)
(Ins. in Charge)
|
Course Goal / Objective
To teach the concept of matrix in detail and to show its application areas.
Course Content
Linear Equations and Matrices, Solution of Linear Systems, Determinants, Real Vector Spaces, Linear Transformations and Matrices, Eigenvalues and Eigenvectors
Course Precondition
no prerequisites
Resources
Uygulamalı Lineer Cebir - Bernard Kolman, David. R. Hill
Notes
Makaleler
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 |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Explains contemporary concepts about Econometrics, Statistics, and Operation Research | 3 |
| PLO02 | Bilgi - Kuramsal, Olgusal | Explains relationships between acquired knowledge about Econometrics, Statistics, and Operation Research | 3 |
| PLO03 | Bilgi - Kuramsal, Olgusal | Explains how to apply acquired knowledge in the field to Economics, Business, and other social sciences | 1 |
| PLO04 | Beceriler - Bilişsel, Uygulamalı | Performs conceptual analysis to develop solutions to problems | 4 |
| PLO05 | Beceriler - Bilişsel, Uygulamalı | Models problems with Mathematics, Statistics, and Econometrics | |
| PLO06 | Beceriler - Bilişsel, Uygulamalı | Interprets the results obtained from the most appropriate method to predict the model | 1 |
| PLO07 | Beceriler - Bilişsel, Uygulamalı | Synthesizes the information obtained by using different sources within the framework of academic rules in a field that does not research | |
| PLO08 | Beceriler - Bilişsel, Uygulamalı | Uses acquired knowledge in the field to determine the vision, aim, and goals for an organization/institution | |
| PLO09 | Beceriler - Bilişsel, Uygulamalı | Searches for new approaches and methods to solve problems being faced | 3 |
| PLO10 | Beceriler - Bilişsel, Uygulamalı | Presents analysis results conveniently | |
| PLO11 | Beceriler - Bilişsel, Uygulamalı | Collects/analyzes data in a purposeful way | |
| PLO12 | Yetkinlikler - İletişim ve Sosyal Yetkinlik | Converts its findings into a master's thesis or a professional report in Turkish or a foreign language | |
| PLO13 | Beceriler - Bilişsel, Uygulamalı | Develops solutions for organizations using Econometrics, Statistics, and Operation Research | |
| PLO14 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Performs an individual work to solve a problem with Econometrics, Statistics, and Operation Research | |
| PLO15 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Leads by taking responsibility individually and/or within the team | |
| PLO16 | 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 | |
| PLO17 | Yetkinlikler - İletişim ve Sosyal Yetkinlik | Uses a package program of Econometrics, Statistics, and Operation Research or writes a new code | |
| PLO18 | 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 | |
| PLO19 | Yetkinlikler - Alana Özgü Yetkinlik | Interprets data on economic and social events by following current issues | |
| PLO20 | Yetkinlikler - Alana Özgü Yetkinlik | Applies social, scientific and professional ethical values | 5 |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Notations and definitions ( determinant, rank, trace, qadratic forms, orthogonal martices) | Students will be prepared by studying relevant subjects from source books according to the weekly program | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Gösterip Yaptırma, Problem Çözme |
| 2 | Similar matrices, Symmetric matrices | Students will be prepared by studying relevant subjects from source books according to the weekly program | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma, Gösterip Yaptırma |
| 3 | Eigenvectors and eigenvalues | Students will be prepared by studying relevant subjects from source books according to the weekly program | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Alıştırma ve Uygulama, Gösterip Yaptırma |
| 4 | Vector space, vector subspace, basis of a vector space, column and null space of a marrix | Students will be prepared by studying relevant subjects from source books according to the weekly program | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Alıştırma ve Uygulama, Gösterip Yaptırma |
| 5 | Basic theorems of generalized inverse | Students will be prepared by studying relevant subjects from source books according to the weekly program | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Alıştırma ve Uygulama, Gösterip Yaptırma |
| 6 | Computing formulas for the g-inverse | Students will be prepared by studying relevant subjects from source books according to the weekly program | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Alıştırma ve Uygulama, Gösterip Yaptırma |
| 7 | Conditional inverse, Hermite form of matrices | Students will be prepared by studying relevant subjects from source books according to the weekly program | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama, Soru-Cevap, Problem Çözme |
| 8 | Mid-Term Exam | Students will be prepared by studying relevant subjects from source books according to the weekly program | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | solutions to systems of linear equations | Students will be prepared by studying relevant subjects from source books according to the weekly program | Öğretim Yöntemleri: Anlatım |
| 10 | Approximate solutions to inconsitent systems of linear equations, Least squares | Students will be prepared by studying relevant subjects from source books according to the weekly program | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Alıştırma ve Uygulama, Gösterip Yaptırma |
| 11 | Pattern matrices | Students will be prepared by studying relevant subjects from source books according to the weekly program | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Alıştırma ve Uygulama, Gösterip Yaptırma, Problem Çözme |
| 12 | Trace of matrik and its properties | Students will be prepared by studying relevant subjects from source books according to the weekly program | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma, Alıştırma ve Uygulama, Gösterip Yaptırma |
| 13 | Matrix derivatives | Students will be prepared by studying relevant subjects from source books according to the weekly program | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Gösterip Yaptırma, Alıştırma ve Uygulama |
| 14 | nnd matrices and its properties | Students will be prepared by studying relevant subjects from source books according to the weekly program | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Alıştırma ve Uygulama, Gösterip Yaptırma |
| 15 | pd and nnd matrices and its properties | Students will be prepared by studying relevant subjects from source books according to the weekly program | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Alıştırma ve Uygulama, Gösterip Yaptırma |
| 16 | Term Exams | Students will be prepared by studying relevant subjects from source books according to the weekly program | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | Students will be prepared by studying relevant subjects from source books according to the weekly program | Ölçme Yöntemleri: Yazılı Sınav |
Student Workload - ECTS
| Works | Number | Time (Hour) | Workload (Hour) |
|---|---|---|---|
| Course Related Works | |||
| Class Time (Exam weeks are excluded) | 14 | 3 | 42 |
| Out of Class Study (Preliminary Work, Practice) | 14 | 5 | 70 |
| Assesment Related Works | |||
| Homeworks, Projects, Others | 0 | 0 | 0 |
| Mid-term Exams (Written, Oral, etc.) | 1 | 15 | 15 |
| Final Exam | 1 | 30 | 30 |
| Total Workload (Hour) | 157 | ||
| Total Workload / 25 (h) | 6,28 | ||
| ECTS | 6 ECTS | ||