Course Name Code Semester T+U Hours Credit ECTS
Matrix Analysis MAT 523 0 3 + 0 3 6
Precondition Courses Students are assumed to be familiar with Analysis I-II and Linear Algebra I-II
Recommended Optional Courses
Course Language Turkish
Course Level yuksek_lisans
Course Type Optional
Course Coordinator Prof.Dr. HALİM ÖZDEMİR
Course Lecturers
Course Assistants Res. Assist. Emre Kişi and Res. Assist. Tuğba Petik
Course Category Field Proper Education
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 the reader to the study of matrix theory, a field which with a great deal of justice may be called the arithmetic of higher mathematics.
Course Content Maximization, minimization, and motivation. Vectors and matrices. Diagonalization and canonical forms. Reduction of general symmetric matrices. The Cayley-Hamilton Theorem for symmetric matrices. Constrained maxima. Functions of matrices. Variational description of characteristic roots. Inequalities. Dynamic programming.
# Course Learning Outcomes Teaching Methods Assessment Methods
1 He/she consolidates the culture of linear algebra. Lecture, Question-Answer, Discussion, Testing, Homework,
2 He/she sees some of usefulness and easiness which are supplied by matrix analysis in mathematical analysis. Lecture, Question-Answer, Discussion, Drilland Practice, Problem Solving, Testing, Homework,
3 To recognize the necessity of matrix analysis in engineering and other applied sciences. Question-Answer, Discussion, Drilland Practice, Problem Solving, Testing, Homework,
4 He/she understands diagonalization in matrices. Question-Answer, Discussion, Drilland Practice, Problem Solving, Testing, Homework,
5 He/she maximizes or minimizes any multivariate function using matrices. Lecture, Question-Answer, Discussion, Drilland Practice, Problem Solving, Testing, Homework,
6 He/she analyzes matrix functions Question-Answer, Discussion, Drilland Practice, Problem Solving, Testing, Homework,
7 He/she finds eigenvalues and eigenvectors of any given matrix Lecture, Question-Answer, Discussion, Drilland Practice, Problem Solving, Testing, Homework,
8 He/she understands inequalities of matrices Lecture, Question-Answer, Discussion, Drilland Practice, Problem Solving, Testing, Homework,
9 He/she solves various inequalities of matrices problems using packet programs Question-Answer, Discussion, Drilland Practice, Problem Solving, Testing, Homework,
Week Course Topics Preliminary Preparation
1 Maximization, minimization, and motivation [1] pages 1-12
2 Vectors and matrices [1] pages 12-32
3 Vectors and matrices (continuation) [1] pages 12-32
4 Diagonalization and canonical forms [1] pages 32-44
5 Reduction of general symmetric matrices [1] pages 44-55
6 Reduction of general symmetric matrices (continuation) [1] pages 44-55
7 The Cayley-Hamilton Theorem for symmetric matrices [1] pages 55-73
8 Constrained maxima [1] pages 73-90
9 Functions of matrices [1] pages 90-112
10 Variational description of characteristic roots [1] pages 112-126
11 Inequalities [1] pages 126-144
12 Inequalities (continuation) [1] pages 126-144
13 Dynamic programming [1] pages 144-157
14 Dynamic programming (continuation) [1] pages 144-157
Resources
Course Notes [1] Bellman, R., Introduction to Matrix Analysis, The Rand Corporation, Philadelphia, 1997.
Course Resources [2] Golub G. H., Van Loan, C. F., Matrix Computations, The Johns Hopkins University Press, London, 1996.

[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
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
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
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
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
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
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
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
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
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. Ödev 100
Total 100
1. Final 70
1. Yıl İçinin Başarıya 30
Total 100
ECTS - Workload Activity Quantity Time (Hours) Total Workload (Hours)
Course Duration (Including the exam week: 16x Total course hours) 16 3 48
Hours for off-the-classroom study (Pre-study, practice) 16 3 48
Mid-terms 1 15 15
Assignment 1 8 8
Performance Task (Seminar) 1 20 20
Final examination 1 20 20
Total Workload 159
Total Workload / 25 (Hours) 6.36
dersAKTSKredisi 6