Course Name Code Semester T+U Hours Credit ECTS
Matrices In Applied Sciences II MAT 570 0 3 + 0 3 6
 Precondition Courses Students are assumed to be familiar with Linear Algebra, Probability, Statistics, Generalized and Conditional Inverse, and Applied Matrix Equations. Recommended Optional Courses Course Language Turkish Course Level yuksek_lisans Course Type Optional Course Coordinator Doç.Dr. MURAT SARDUVAN Course Lecturers Doç.Dr. MURAT SARDUVAN, Course Assistants Res. Assist. Emre KİŞİ- Res. Assist. Tuğba PETİK Course Category Course Objective Linear algebra and matrix theory have long been fundamental tools in mathematical and statistical disciplines as well as applied sciences for example, sociology, education, chemistry, and engineering for research in their own right. The aim of this course is to introduce some information and facilities related to special types of matrices mainly used in many applied sciences. Course Content Transformation of Random Variables, Multivariate Normal Density; Moments of Density Functions and Excepted Values of Random Matrices, Marginal Density Functions, Expected Values of Quadratic Forms, Expectation of the Elements of a Wishart Matrix, Matrices with Positive Principle Minors and Matrices with Non-Positive Off Diagonal Elements; Nonnegative Matrices; Idempotent Matrices and Tripotent Matrices; Projections and Additional Theorems.
# Course Learning Outcomes Teaching Methods Assessment Methods
1 He/she consolidates the cultures of random variable and multivariate normal density. Lecture, Question-Answer, Discussion, Testing, Homework,
2 He/she sees the concepts of random matrices and their expected values. Lecture, Question-Answer, Discussion, Drilland Practice, Problem Solving, Testing, Homework, Project / Design,
3 He/she recognizes usefulness of quadratic forms with normal density. Question-Answer, Discussion, Drilland Practice, Problem Solving, Testing, Homework,
4 He/she recognizes usefulness of matrices with positive principle minor. Question-Answer, Discussion, Drilland Practice, Problem Solving, Testing, Homework,
5 He/she understands the concept of M-matrices and Z-matrices. Lecture, Question-Answer, Discussion, Drilland Practice, Problem Solving, Testing, Homework, Project / Design,
6 He/she recognizes usefulness of nonnegative matrices. Question-Answer, Discussion, Drilland Practice, Problem Solving, Testing, Homework,
7 He/she recognizes usefulness of idempotent and tripotent matrices. Question-Answer, Discussion, Drilland Practice, Problem Solving, Testing, Homework,
Week Course Topics Preliminary Preparation
1 Transformation of Random Variables, Multivariate Normal Density [1] pages 326-334
2 Moments of Density Functions and Expected Values of Random Matrices [1] pages 335-344
3 Marginal Density Functions [1] pages 345-360
4 Expected Values of Quadratic Forms [1] pages 361-368
5 Expectation of the Elements of a Wishart Matrix and Problems [1] pages 369-372
6 Matrices with Positive Principle Minors [1] pages 373-378
7 Matrices with Non-Positive Off Diagonal Elements [1] pages 379-381
8 M- matrices with Positive and Non-positive Principle Minors [1] pages 382-387
9 Z-matrices with Positive and Non-positive Principle Minors [1] pages 388-393
10 Nonnegative Matrices [1] pages 394-417
11 Idempotent Matrices [1] pages 418-429
12 Tripotent Matrices [1] pages 430-434
13 Projections [1] pages 435-438
14 Additional Theorems [1] pages 439-450
Resources
Course Notes Graybill, F. A., Introduction to Matrices with Applications in Statistics, United States, 1969.
Course Resources [1] Searle, S. R., Matrix Algebra Useful For Statistics, Canada, 1982.
[2] Johnson, R. A. and Wichern, D. W., Applied Multivariate Statistical Analysis, Englewood Cliffs, New Jersey, 1982.
[3] Horn, R. A., Johnson, C. R., Matrix Analysis, Cambridge University Press, Cambridge, 1985.
Order Program Outcomes Level of Contribution
1 2 3 4 5
0 Develop strategic, political and practice plans and evaluate the results by taking into account the quality process in his/her area of expertise X
2 Student follows the current journals in his/her field and puts forward problems. X
3 Student understands the relations between the disciplines pertaining to the undergraduate programs of Mathematics X
4 Student gets new knowledge by relating the already acquired experience and knowledge with the subject-matters out of his/her field. X
5 Student uses different proof methods to come to a solution by analyzing the problems encountered. X
6 Student determines the problems to be solved within his/her field and if necessary takes the lead. X
7 Student conveys, in team work, his/her knowledge in the studies done in different disciplines by applying the dynamics pertaining to his/her own field. X
8 Student critically evaluates the knowledge got at the bachelor´s degree level, makes up the missing knowledge and focuses on the current subject-matters X
9 Student knows a foreign language to communicate orally and in writing and uses the foreign language in a way that he/she can have a command of the Maths terminology and can do a source research. X
10 Student improves himself/herself at a level of expertness in Mathematics or in the fields of application by improving the knowledge got at the bachelor´s degree level. X
11 Student considers the scientific and cultural ethical values in the phases of gathering and conveying data or writing articles. X
Evaluation System
Semester Studies Contribution Rate
1. Ara Sınav 50
1. Ödev 50
Total 100
1. Yıl İçinin Başarıya 50
1. Final 50
Total 100