Matrix Analysis (MATH333) Course Detail

Course Name	Course Code	Season	Lecture Hours	Application Hours	Lab Hours	Credit	ECTS
Matrix Analysis	MATH333	Area Elective	3	0	0	3	6

Pre-requisite Course(s)
(MATH231 veya MATH275)

Course Language	English
Course Type	Elective Courses
Course Level	Natural & Applied Sciences Master's Degree
Mode of Delivery	Face To Face
Learning and Teaching Strategies	Lecture, Question and Answer, Drill and Practice.
Course Coordinator
Course Lecturer(s)
Course Assistants
Course Objectives	Linear algebra and matrix theory have been fundamental tools in mathematical disciplines. Having the basic knowlegde and properties of linear transformations, vector spaces, vectors and matrices the aim is to present classical and recent results of matrix analysis that have proved to be important to applied mathematics.
Course Learning Outcomes	The students who succeeded in this course; understand Gersgorin’s Circle Theorem and related theorems, and use them, determine whether a given family is simultaneously diagonalizable or not, understand Schur’s Theorem and use it for the triangularization of a matrix, understand Normal matrices, Hermitian matrices and their properties, and perform the QR factorization, triangular factorizations, LU decompositions, determine the minimal polynomials and possible canonical forms of matrices, understand vector and matrix norms, and their properties and using matrix norms determine bounds for the spectral radiuses of matrices, understand the effect of perturbations in the solution of systems of linear equations, understand the Singular Value Decomposition and its properties and use it, understand Positive-Negative Definite matrices, nonnegative matrices and their properties, and conditions for the irreducibility of nonnegative matrices.
Course Content	Preliminaries, eigenvalues, eigenvectors and similarity, unitary equivalence and normal matrices, Canonical forms, Hermitian and symmetric matrices, norms for vectors and matrices, location and perturbation of eigenvalues, positive definite matrices, nonnegative matrices.

Weekly Subjects and Releated Preparation Studies

Week	Subjects	Preparation
1	Vector Spaces, Matrices, Determinants, Rank, Nonsingularity, The Usual Inner Product, Partitioned Matrices	pp. 1-18
2	The Eigenvalue-Eigenvector Equation, The Characteristic Polynomial, Similarity	pp. 33-57
3	Unitary Matrices, Unitary Equivalence	pp. 65-78
4	Schur’s Unitary Triangularization Theorem, Normal Matrices	pp. 79-111
5	The Jordan Canonical Form, Polynomials and Matrices, The Minimal Polynomial	pp. 119-149
6	Triangular Factorization, LU Decomposition	pp. 158-166
7	Hermitian Matrices, Properties and Characterizations of Hermitian Matrices, Complex Symmetric Matrices	pp. 167-217
8	Defining Properties of Vector Norms and Inner Products, Examles of Vector Norms, Algebraic Properties of Vector Norms	pp. 257-268
9	Matrix Norms, Vector Norms on Matrices, Errors in Inverses and Solutions of Linear Systems	pp. 290-342
10	Gersgorin Discs, Perturbation Theorems, Other Inclusion Regions	pp. 343-390
11	Positive Definite Matrices, Their Properties and Characterizations	pp. 391-410
12	The Polar Form and The SVD, The Schur Product Form, Simultaneous Diagonalization	pp. 411-468
13	Nonnegative Matrices; Inequalities and Generalities, Positive Matrices	pp. 487-502
14	Nonnegative Matrices, Irreducible Nonnnegative Matrices	pp. 503-514
15	General Review
16	Final Exam

Sources

Course Book	1. Matrix Analysis, R.A.Horn & C.R.Johnson, Cambridge University Press, 1991.
Other Sources	2. 1- Matrix Theory; Basic Results and Techniques, By F.Zhang, Springer, 2011
	3. 2- Elementary Linear Algebra, B.Kolman &D.R.Hill, 9th edition, Prentice Hall, 2008.

Evaluation System

Requirements	Number	Percentage of Grade
Attendance/Participation	-	-
Laboratory	-	-
Application	-	-
Field Work	-	-
Special Course Internship	-	-
Quizzes/Studio Critics	-	-
Homework Assignments	5	10
Presentation	-	-
Project	-	-
Report	-	-
Seminar	-	-
Midterms Exams/Midterms Jury	2	55
Final Exam/Final Jury	1	35
Toplam	8	100

Percentage of Semester Work	65
Percentage of Final Work	35
Total	100

Course Category

Core Courses	X
Major Area Courses
Supportive Courses
Media and Managment Skills Courses
Transferable Skill Courses

The Relation Between Course Learning Competencies and Program Qualifications

#	Program Qualifications / Competencies	Level of Contribution
#	Program Qualifications / Competencies	1	2	3	4	5
1	Has the ability to apply scientific knowledge gained in the undergraduate education and to expand and extend knowledge in the same or in a different area.
2	Has the ability to obtain, to evaluate, to interpret and to apply information by doing scientific research.
3	Can apply gained knowledge and problem solving abilities in inter-disciplinary research.
4	Has the ability to work independently within research area, to state the problem, to develop solution techniques, to solve the problem, to evaluate the obtained results and to apply them when necessary.
5	Takes responsibility individually and as a team member to improve systematic approaches to produce solutions in unexpected complicated situations related to the area of study.
6	Can develop strategies, implement plans and principles on the area of study and can evaluate obtained results within the framework.
7	Can develop and extend the knowledge in the area and to use them with scientific, social and ethical responsibility.
8	Has the ability to follow recent developments within the area of research, to support research with scientific arguments and data, to communicate the information on the area of expertise in a systematically by means of written report and oral/visual presentation.
9	Has proficiency in English language and has the ability to communicate with colleagues and to follow the innovations in mathematics and related fields.
10	Has software and hardware knowledge in the area of expertise, and has proficient information and communication technology knowledge.
11	Has professional ethical consciousness and responsibility which takes into account the universal and social dimensions in the process of data collection, interpretation, implementation and declaration of results in mathematics and its applications.

ECTS/Workload Table

Activities	Number	Duration (Hours)	Total Workload
Course Hours (Including Exam Week: 16 x Total Hours)
Laboratory
Application
Special Course Internship
Field Work
Study Hours Out of Class	16	3	48
Presentation/Seminar Prepration
Project
Report
Homework Assignments	5	6	30
Quizzes/Studio Critics
Prepration of Midterm Exams/Midterm Jury	2	15	30
Prepration of Final Exams/Final Jury
Total Workload			108