Nevşehir Hacı Bektaş Veli University Course Catalogue

Information Of Programmes

FACULTY OF LETTERS & SCIENCE / MAT442 - MATHEMATICS

Code: MAT442 Course Title: MATRICES ALGEBRA II Theoretical+Practice: 4+0 ECTS: 6
Year/Semester of Study 4 / Spring Semester
Level of Course 1st Cycle Degree Programme
Type of Course Optional
Department MATHEMATICS
Pre-requisities and Co-requisites None
Mode of Delivery Face to Face
Teaching Period 14 Weeks
Name of Lecturer SEZER SORGUN (ssorgun@nevsehir.edu.tr)
Name of Lecturer(s)
Language of Instruction Turkish
Work Placement(s) None
Objectives of the Course
To present some classes of special matrix.

Learning Outcomes PO MME
The students who succeeded in this course:
LO-1 Can understand the special definite matrices and know their properties. PO-4 Analytically use the interdisciplinary approach at learning process.
Examination
LO-2 Can know quadratic forms for matrices. PO-5 Develop suitable material for a subject on a mathematical area, to use the knowledge and experience gains with different methods
Examination
PO: Programme Outcomes
MME:Method of measurement & Evaluation

Course Contents
Normal matrices, Hernitian matrices, Positive definite matrices, Schur Decomposition, Quadratic form, Rayleigh quotient, Nonnegative matrices, the QR algorithm, Generalized inverses.
Weekly Course Content
Week Subject Learning Activities and Teaching Methods
1 Normal matrices, Hermit matrices, Real symmetric matrices Teaching topic and applications
2 Definete matrices, Tests for positive definiteness matrices, Square roots of matrices, Cholesky decomposition Teaching topic and applications
3 Unitary matrices, Schur decomposition,Elementary reflectors, Summary of similarity transformations Teaching topic and applications
4 Quadratic form,Diagonal form Teaching topic and applications
5 Congruence,Inertia, Rayleigh quotient Teaching topic and applications
6 Nonnegative and positive matrices, Irreducible matrices Teaching topic and applications
7 Primitive matrices, Stochastic matrices, Finite Markov chains Teaching topic and applications
8 mid-term exam
9 Circulant matrices, Band matrices, Teaching topic and applications
10 Tridiagonal matrices, Hessenberg form Teaching topic and applications
11 Numerical methods, The power method, The inverse power method Teaching topic and applications
12 The Shifted inverse power method, Gerschgorin's theorem Teaching topic and applications
13 The modified Gram-Schmidt process, QR decomposition, The QR algorithm, Accelerating convergence Teaching topic and applications
14 Properties, A formula for generalized inverses, Singular-value decomposition Teaching topic and applications
15 A stable formula for the generalized inverse , Least squares solutions Teaching topic and applications
16 final exam
Recommend Course Book / Supplementary Book/Reading
1 Matris işlemleri, R.Bronson, Çeviri Editörü: H.H.Hacısalihoğlu, Schaum's outlines,Nobel yayın dağıtım,1989.
Required Course instruments and materials
The lecture books

Assessment Methods
Type of Assessment Week Hours Weight(%)
mid-term exam 8 2 40
Other assessment methods
1.Oral Examination
2.Quiz
3.Laboratory exam
4.Presentation
5.Report
6.Workshop
7.Performance Project
8.Term Paper
9.Project
final exam 16 2 60

Student Work Load
Type of Work Weekly Hours Number of Weeks Work Load
Weekly Course Hours (Theoretical+Practice) 4 14 56
Outside Class
       a) Reading 2 14 28
       b) Search in internet/Library 3 14 42
       c) Performance Project 0
       d) Prepare a workshop/Presentation/Report 0
       e) Term paper/Project 0
Oral Examination 0
Quiz 0
Laboratory exam 0
Own study for mid-term exam 3 7 21
mid-term exam 2 1 2
Own study for final exam 3 7 21
final exam 2 1 2
0
0
Total work load; 172