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| Course Description |
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| Course Name |
: |
Matrix Theory |
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| Course Code |
: |
İSB471 |
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| Course Type |
: |
Compulsory |
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| Level of Course |
: |
First Cycle |
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| Year of Study |
: |
4 |
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| Course Semester |
: |
Fall (16 Weeks) |
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| ECTS |
: |
4 |
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| Name of Lecturer(s) |
: |
Assoc.Prof.Dr. MAHMUDE REVAN ÖZKALE
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| Learning Outcomes of the Course |
: |
Do matrix operations
Understand the properties of the determinant
Find the inverse of a matrix
Do operations with partitioned matrices
Find the generalized inverse of matrices
Solve linear systems
Find the least squares solution of linear systems
Define linear, bilinear and quadratic forms
Define positive definite, positive semidefinite and nonnegative definite matrices
Derive the linear and quadratic forms
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| Mode of Delivery |
: |
Face-to-Face |
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| Prerequisites and Co-Prerequisites |
: |
None |
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| Recommended Optional Programme Components |
: |
None |
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| Aim(s) of Course |
: |
Use of mathematical techniques that are required for matrix operations and use matrix operations to solve problems that may arise in various fields such as statistics |
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| Course Contents |
: |
Matrix operations, find the determinant and rank of a matrix, partitioned matrices, find the generalized inverse, solution to linear systems, linear, bilinear and quadratic forms and their derivatives, positive definiteness, positice semidefiniteness and nonnegative definiteness of a matrix |
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| Language of Instruction |
: |
Turkish |
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| Work Place |
: |
Faculty of Arts and Sciences Annex Classrooms |
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Course Outline /Schedule (Weekly) Planned Learning Activities |
| Week | Subject | Student's Preliminary Work | Learning Activities and Teaching Methods |
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1 |
Speical matrices and matrix operations |
Source reading |
Lecture |
|
2 |
Linear independence and rank of matrix |
Source reading |
Lecture |
|
3 |
Determinants and determinant properties |
Source reading |
Lecture, problem-solving |
|
4 |
Finding the inverse of a matrix |
Source reading |
Lecture, problem-solving |
|
5 |
Partitioned matrices |
Source reading |
Lecture, problem-solving |
|
6 |
Elementary transformations, echelon form, equivalent matrices |
Source reading |
Lecture, problem-solving |
|
7 |
Moore Penrose inverse and properties |
Source reading |
Lecture |
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8 |
Midterm exam |
Review the topics discussed in the lecture notes and sources |
Written exam |
|
9 |
Generalized inverse |
Source reading |
Lecture, problem-solving |
|
10 |
Systems of linear equations |
Source reading |
Lecture, problem-solving |
|
11 |
Systems of linear equations |
Source reading |
Lecture, problem-solving |
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12 |
Least squares solution to systems of linear equations |
Source reading |
Lecture, problem-solving |
|
13 |
Linear, bilinear and quadratic forms |
Source reading |
Lecture |
|
14 |
Derivatives of linear and quadratic forms |
Source reading |
Lecture, |
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15 |
Kronecker multiplication |
Source reading |
Lecture |
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16/17 |
Final exam |
Review the topics discussed in the lecture notes and sources |
Written exam |
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Required Course Resources |
| Resource Type | Resource Name |
| Recommended Course Material(s) |
 1. Schott, J. R. (2005), Matrix Analysis for Statistics. John Wiley & Sons
2. Harville, D. A. (1997), Matrix Algebra from a Statistician’s Perspective. Springer Verlag
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| |
| Required Course Material(s) | |
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Assessment Methods and Assessment Criteria |
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Semester/Year Assessments |
Number |
Contribution Percentage |
|
Mid-term Exams (Written, Oral, etc.) |
1 |
100 |
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Homeworks/Projects/Others |
0 |
0 |
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Total |
100 |
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Rate of Semester/Year Assessments to Success |
40 |
| |
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Final Assessments
|
100 |
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Rate of Final Assessments to Success
|
60 |
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Total |
100 |
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| Contribution of the Course to Key Learning Outcomes |
| # | Key Learning Outcome | Contribution* |
|
1 |
Utilize computer systems and softwares |
0 |
|
2 |
Apply the statistical analyze methods |
2 |
|
3 |
Make statistical inference(estimation, hypothesis tests etc.) |
0 |
|
4 |
Generate solutions for the problems in other disciplines by using statistical techniques |
1 |
|
5 |
Discover the visual, database and web programming techniques and posses the ability of writing programme |
0 |
|
6 |
Construct a model and analyze it by using statistical packages |
1 |
|
7 |
Distinguish the difference between the statistical methods |
1 |
|
8 |
Be aware of the interaction between the disciplines related to statistics |
2 |
|
9 |
Make oral and visual presentation for the results of statistical methods |
1 |
|
10 |
Have capability on effective and productive work in a group and individually |
1 |
|
11 |
Develop scientific and ethical values in the fields of statistics-and scientific data collection |
1 |
|
12 |
Explain the essence fundamentals and concepts in the field of Probability, Statistics and Mathematics |
3 |
|
13 |
Emphasize the importance of Statistics in life |
2 |
|
14 |
Define basic principles and concepts in the field of Law and Economics |
0 |
|
15 |
Produce numeric and statistical solutions in order to overcome the problems |
4 |
|
16 |
Construct the model, solve and interpret the results by using mathematical and statistical tehniques for the problems that include random events |
2 |
|
17 |
Use proper methods and techniques to gather and/or to arrange the data |
1 |
|
18 |
Professional development in accordance with their interests and abilities, as well as the scientific, cultural, artistic and social fields, constantly improve themselves by identifying training needs |
0 |
| * Contribution levels are between 0 (not) and 5 (maximum). |
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| Student Workload - ECTS |
| Works | Number | Time (Hour) | Total Workload (Hour) |
| Course Related Works |
|
Class Time (Exam weeks are excluded) |
14 |
3 |
42 |
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Out of Class Study (Preliminary Work, Practice) |
14 |
3 |
42 |
| Assesment Related Works |
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Homeworks, Projects, Others |
0 |
0 |
0 |
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Mid-term Exams (Written, Oral, etc.) |
1 |
10 |
10 |
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Final Exam |
1 |
18 |
18 |
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Total Workload: | 112 |
| Total Workload / 25 (h): | 4.48 |
| ECTS Credit: | 4 |
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