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	Technical Elective Courses
Course Level	Bachelor’s Degree (First Cycle)
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	Adequate knowledge in mathematics, science and subjects specific to the software engineering discipline; the ability to apply theoretical and practical knowledge of these areas to complex engineering problems.		X
2	The ability to identify, define, formulate and solve complex engineering problems; selecting and applying proper analysis and modeling techniques for this purpose.
3	The ability to design a complex system, process, device or product under realistic constraints and conditions to meet specific requirements; the ability to apply modern design methods for this purpose.
4	The ability to develop, select and utilize modern techniques and tools essential for the analysis and determination of complex problems in software engineering applications; the ability to utilize information technologies effectively.
5	The ability to gather data, analyze and interpret results for the investigation of complex engineering problems or research topics specific to the software engineering discipline.
6	The ability to work effectively in inter/inner disciplinary teams; ability to work individually.
7	Effective oral and written communication skills in Turkish; the ability to write effective reports and comprehend written reports, to prepare design and production reports, to make effective presentations, to give and receive clear and understandable instructions.
8	The knowledge of at least one foreign language; the ability to write effective reports and comprehend written reports, to prepare design and production reports, to make effective presentations, to give and receive clear and understandable instructions.
9	Recognition of the need for lifelong learning; the ability to access information and follow recent developments in science and technology with continuous self-development
10	The ability to behave according to ethical principles, awareness of professional and ethical responsibility.
11	Knowledge of the standards utilized in software engineering applications.
12	Knowledge on business practices such as project management, risk management and change management.
13	Awareness about entrepreneurship, and innovation.
14	Knowledge on sustainable development.
15	Knowledge of the effects of software engineering applications on the universal and social dimensions of health, environment, and safety.
16	Awareness of the legal consequences of engineering solutions.
17	An ability to apply algorithmic principles, mathematical foundations, and computer science theory in the modeling and design of computer-based systems with the trade-offs involved in design choices.
18	The ability to apply engineering approach to the development of software systems by analyzing, designing, implementing, verifying, validating and maintaining software systems.

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