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Information
| Code | ISB501 |
| Name | Matrix Theory |
| Term | 2023-2024 Academic Year |
| Semester | . Semester |
| 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 | Prof. Dr. SADULLAH SAKALLIOĞLU |
Course Goal / Objective
To provide the students with the necessary information in linear models and multivariate analysis.
Course Content
Basic terms and concepts in the matrix theory, column space, null space, subspace, and Echelon form, type of mxn matrices g-inverse, solution of systems of equations, matrix derivative and properties of positive definit and nnd matrices.
Course Precondition
None
Resources
Franklin A. Graybill (1983), Matrices with Applications in Statistics, Wadsworth International Group, Belmont, California.
Notes
James R. Schott (2005), Matrix Analysis for Statistics, John Wiley and Sons Inc. New Jersey
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Understand the fundamental rules and concepts of matrix |
| LO02 | Define the concepts of linear independence, eigenvalues and eigenvectors |
| LO03 | Learn the concepts of vector space, column space, null space, subspace and reduce to echelon form, |
| LO04 | Gain the findings regarding the inverse of a matrix and know the properties of g inverse |
| LO05 | Have the ability to apply patterned matrices |
| LO06 | Solve the systems of equations and examine the terms of consistency |
| LO07 | Comprehend matrix trace and its properties |
| LO08 | Have the knowedge about matix derivative, and properties of positive definit and n.n.d. matrices |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Have in-depth theoretical and practical knowledge about Probability and Statistics | |
| PLO02 | Bilgi - Kuramsal, Olgusal | They have the knowledge to make doctoral plans in the field of statistics. | 3 |
| PLO03 | Bilgi - Kuramsal, Olgusal | Has comprehensive knowledge about analysis and modeling methods used in statistics. | 4 |
| PLO04 | Bilgi - Kuramsal, Olgusal | Has comprehensive knowledge of methods used in statistics. | 3 |
| PLO05 | Bilgi - Kuramsal, Olgusal | Make scientific research on Mathematics, Probability and Statistics. | 3 |
| PLO06 | Bilgi - Kuramsal, Olgusal | Indicates statistical problems, develops methods to solve. | 4 |
| PLO07 | Bilgi - Kuramsal, Olgusal | Apply innovative methods to analyze statistical problems. | 4 |
| PLO08 | Bilgi - Kuramsal, Olgusal | Designs and applies the problems faced in the field of analytical modeling and experimental researches. | 3 |
| PLO09 | Bilgi - Kuramsal, Olgusal | Access to information and do research about the source. | 3 |
| PLO10 | Bilgi - Kuramsal, Olgusal | Develops solution approaches in complex situations and takes responsibility. | 2 |
| PLO11 | Bilgi - Kuramsal, Olgusal | Has the confidence to take responsibility. | 3 |
| PLO12 | Beceriler - Bilişsel, Uygulamalı | They demonstrate being aware of the new and developing practices. | |
| PLO13 | Beceriler - Bilişsel, Uygulamalı | He/She constantly renews himself/herself in statistics and related fields. | 2 |
| PLO14 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Communicate in Turkish and English verbally and in writing. | 3 |
| PLO15 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Transmits the processes and results of their studies clearly in written and oral form in national and international environments. | 2 |
| PLO16 | Yetkinlikler - Öğrenme Yetkinliği | It considers the social, scientific and ethical values in the collection, processing, use, interpretation and announcement stages of data and in all professional activities. | 3 |
| PLO17 | Yetkinlikler - Öğrenme Yetkinliği | Uses the hardware and software required for statistical applications. |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Notations and definitions ( determinant, rank, trace, qadratic forms, orthogonal martices) | Reading the related references | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 2 | Similar matrices, Symmetric matrices | Reading the related references | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 3 | Eigenvectors and eigenvalues | Reading the related references | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 4 | Vector space, vector subspace, basis of a vector space, column and null space of a marrix | Reading the related references | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 5 | Basic theorems of generalized inverse | Reading the related references | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 6 | Computing formulas for the g-inverse | Reading the related references | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 7 | Conditional inverse, Hermite form of matrices | Reading the related references | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 8 | Mid-Term Exam | Review the topics discussed in the lecture notes and references | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | solutions to systems of linear equations, | Reading the related references | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 10 | Approximate solutions to inconsitent systems of linear equations, solutions of least squares | Reading the related references | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 11 | Pattern matrices | Reading the related references | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 12 | Trace of matrik and its properties | Reading the related references | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 13 | Matrix derivatives | Reading the related references | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 14 | nnd matrices and its properties | Reading the related references | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 15 | Pd and nnd matrices and its properties | Reading the related references | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 16 | Term Exams | Review the topics discussed in the lecture notes and sources | Ölçme Yöntemleri: Yazılı Sınav, Ödev, Performans Değerlendirmesi |
| 17 | Term Exams | Review the topics discussed in the lecture notes and sources | Ölçme Yöntemleri: Yazılı Sınav, Ödev, Performans Değerlendirmesi |
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 | ||