DEGREE PROGRAMS  Associate's Degree (Short Cycle)  Bachelor’s Degree (First Cycle)  Master’s Degree (Second Cycle)

Course Description Course Name : Matrix Theory Course Code : ISB-501 Course Type : Optional Level of Course : Second Cycle Year of Study : 1 Course Semester : Fall (16 Weeks) ECTS : 6 Name of Lecturer(s) : Prof.Dr. SADULLAH SAKALLIOĞLU Learning Outcomes of the Course : Understand the fundamental rules and concepts of matrix Define the concepts of linear independence, eigenvalues and eigenvectors Learn the concepts of vector space, column space, null space, subspace and reduce to echelon form, Gain the findings regarding the inverse of a matrix and know the properties of g inverse Have the ability to apply patterned matrices Solve the systems of equations and examine the terms of consistency Comprehend matrix trace and its properties Have the knowedge about matix derivative, and properties of positive definit and n.n.d. matrices Mode of Delivery : Face-to-Face Prerequisites and Co-Prerequisites : None Recommended Optional Programme Components : None Aim(s) of Course : To provide the students with the necessary information in linear models and multivariate analysis Course Contents : 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. Language of Instruction : Turkish Work Place : Seminar room   Course Outline /Schedule (Weekly) Planned Learning Activities Week Subject Student's Preliminary Work Learning Activities and Teaching Methods 1 Notations and definitions ( determinant, rank, trace, qadratic forms, orthogonal martices) Reading the related references Lecture, discussion 2 Similar matrices, Symmetric matrices Reading the related references Lecture, discussion 3 Eigenvectors and eigenvalues Reading the related references Lecture, discussion 4 Vector space, vector subspace, basis of a vector space, column and null space of a marrix Reading the related references Lecture, discussion 5 Basic theorems of generalized inverse Reading the related references Lecture, discussion 6 Computing formulas for the g-inverse Reading the related references Lecture, discussion 7 Conditional inverse, Hermite form of matrices Reading the related references Lecture, discussion 8 Midterm exam Review the topics discussed in the lecture notes and references Written Exam / Homework 9 solutions to systems of linear equations, Reading the related references Lecture, discussion 10 Approximate solutions to inconsitent systems of linear equations, Least squares Reading the related references Lecture, discussion 11 Pattern matrices Reading the related references Lecture, discussion 12 Trace of matrik and its properties Reading the related references Lecture, discussion 13 Matrix derivatives Reading the related references Lecture, discussion 14 nnd matrices and its properties Reading the related references Lecture, discussion 15 pd and nnd matrices and its properties Reading the related references Lecture, discussion 16/17 Final exam Review the topics discussed in the lecture notes and sources Written Exam   Required Course Resources Resource Type Resource Name Recommended Course Material(s)  Franklin A. Graybill (1983), Matrices with Applications in Statistics, Wadsworth International Group, Belmont, California. Required Course Material(s)  James R. Schott (2005), Matrix Analysis for Statistics, John Wiley and Sons Inc. New Jersey.   Assessment Methods and Assessment Criteria Semester/Year Assessments Number Contribution Percentage     Mid-term Exams (Written, Oral, etc.) 1 60     Homeworks/Projects/Others 3 40 Total 100 Rate of Semester/Year Assessments to Success 40   Final Assessments 100 Rate of Final Assessments to Success 60 Total 100   Contribution of the Course to Key Learning Outcomes # Key Learning Outcome Contribution* 1 Possess advanced level of theoretical and applicable knowledge in the field of Probability and Statistics. 1 2 Conduct scientific research on Mathematics, Probability and Statistics. 3 3 Possess information, skills and competencies necessary to pursue a PhD degree in the field of Statistics. 3 4 Possess comprehensive information on the analysis and modeling methods used in Statistics. 0 5 Present the methods used in analysis and modeling in the field of Statistics. 0 6 Discuss the problems in the field of Statistics. 4 7 Implement innovative methods for resolving problems in the field of Statistics. 4 8 Develop analytical modeling and experimental research designs to implement solutions. 3 9 Gather data in order to complete a research. 3 10 Develop approaches for solving complex problems by taking responsibility. 2 11 Take responsibility with self-confidence. 3 12 Have the awareness of new and emerging applications in the profession 0 13 Present the results of their studies at national and international environments clearly in oral or written form. 0 14 Oversee the scientific and ethical values during data collection, analysis, interpretation and announcment of the findings. 0 15 Update his/her knowledge and skills in statistics and related fields continously 2 16 Communicate effectively in oral and written form both in Turkish and English. 3 17 Use hardware and software required for statistical applications. 0 * Contribution levels are between 0 (not) and 5 (maximum).   Student Workload - ECTS Works Number Time (Hour) Total Workload (Hour) Course Related Works     Class Time (Exam weeks are excluded) 14 3 42     Out of Class Study (Preliminary Work, Practice) 14 3 42 Assesment Related Works     Homeworks, Projects, Others 3 8 24     Mid-term Exams (Written, Oral, etc.) 1 15 15     Final Exam 1 20 20 Total Workload: 143 Total Workload / 25 (h): 5.72 ECTS Credit: 6