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Information
| Code | IEM717 |
| Name | Vector Spaces II |
| Term | 2022-2023 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 | Doç. Dr. ERSİN KIRAL |
Course Goal / Objective
To give insight and skill about the concrete aspects of linear algebra,To provide basic concepts of matrices and the systems of homogeny and linear equations,To solve the systems using matrices,To teach vector spaces and abstract mathematical concepts,To teach abstract thought
Course Content
Linear systems relationship between matrices and linear systems,Row-matrice operators and solvind linear systems,vector spaces and subspaces,bases, dimensions and coordinates,Linear transformations and The algebra of linear transformations,linear functionals,dual spaces,annihilating polynomials,Lagrange interpolation,commutative rings and determinant function,permutations.
Course Precondition
Resources
Notes
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Knows the properties of the determinant function |
| LO02 | gives some special examples of linear transformations and proves some important theorems about linear transformations |
| LO03 | knows about very simple triangular and diagonal forms of linear transformations |
| LO04 | Finds out minimal polynomial.By determininig the class of the annihilating polynomials of linear transformation . Calculates the Jordan form of the linear transformation |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Explains contemporary concepts about Econometrics, Statistics, and Operation Research | |
| PLO02 | Bilgi - Kuramsal, Olgusal | Explains relationships between acquired knowledge about Econometrics, Statistics, and Operation Research | |
| PLO03 | Bilgi - Kuramsal, Olgusal | Explains how to apply acquired knowledge in the field to Economics, Business, and other social sciences | |
| PLO04 | Beceriler - Bilişsel, Uygulamalı | Performs conceptual analysis to develop solutions to problems | |
| 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 | |
| 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 | |
| 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 |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Applications of determinant function | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 2 | Uniqueness of determinant and some properties of determinant | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 3 | Eigenvalues and eigenvectors | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 4 | Annihilating polynomials and invariant subalgebras | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 5 | Diagonalizations and triangulation | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 6 | Direct-sum decompositions | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 7 | Invariant direct sums and The Primary Decomposition Theorem | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 8 | Mid-Term Exam | Review of the relevant pages from sources | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Cyclic subspaces and annihilators | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 10 | Cyclic Decompositions | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 11 | Jordan Form | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 12 | Inner products | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 13 | Inner product spaces | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 14 | Orthogonality and orthogonal complement | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 15 | Orthogonality and orthogonal complement | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 16 | Term Exams | Review of the relevant pages from sources | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | Review of the relevant pages from sources | Ölçme Yöntemleri: Yazılı Sınav |