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Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS MAT 5031 MATRIX THEORY ELECTIVE 3 0 0 7

Offered By

Graduate School of Natural and Applied Sciences

Level of Course Unit

Second Cycle Programmes (Master's Degree)

Course Coordinator

ASSOCIATE PROFESSOR MUSTAFA ÖZEL

Offered to

Mathematics Mathematics

Course Objective

This course will cover the fundamental ideas, results and the techniques in matrix theory. It will present the various matrix norms, canonical forms and their applications.

Learning Outcomes of the Course Unit

1   will be able to understand the basic theory and techniques in linear algebra 2   will be able to understand the diagonalizability and triangularization 3   will be able to understand the generalized inverses and g-inverse of block matrices 4   will be able to understand the matrix polynomials and canonical forms 5   will be able to understand the vector and matrix norms 6   will be able to understand the positive definite matrices and singular value decomposition

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description 1 Vector spaces, Matrices, Determinants, Rank, Span, Basis and Dimension 2 Eigenvalues, Eigenvectors, Characteristic Polynomial and Equation, Spectral Radius 3 Gerschgorin Circles, Similarity, Diagonalizability, Schur Triangularization 4 Generalized Inverse, Generalized Inverse of Special Matrices, Computing Formulas for g-inverse, Systems of Linear Equations 5 Approximate Solutions to Inconsistent Systems of Linear Equations, Special Matrix Products: Kronecker, Hadamard, Rao, and Tracy-Sing Products 6 Unitary Matrices, Unitary Equivalence 7 Midterm 8 Gram-Schmidth and Modified Gram Schmidth Algorithm, QR Factorization 9 Matrix Polynomials, Right and Left Division of Matrix Polynomials, the Generalized Bézout Theorem 10 Minimal Polynomial of a Matrix, Invariant Polynomials and Elementary Divisors, Jordan form, Polynomials and Matrices, other Canonical Forms 11 Vector norms, p-norms, Matrix Norms; Frobenius Matrix Norm, General Matrix Norms, Induced Matrix Norms, Positive Definite Matrices 12 Singular Value Decomposition, Variational Characterizations of Eigenvalues

Recomended or Required Reading

Textbook(s) -R.A. Horn, Matrix Analysis, Cambridge University Press 1996. ISBN: 0-521-38632-2 Supplementary Book(s) -C.D. Meyer, Matrix Analysis and Applied Linear Algebra SIAM 2001 ISBN 0-89871-454-0. -C.R.Rao & S.K.Mitra, Generalized Inverse of Matrices and Its Applications, John Wiley & Sons, 1971, ISBN: 0-471-70821-6

Planned Learning Activities and Teaching Methods

Lecture notes Presentation Problem solving

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA 1 ASG ASSIGNMENT 2 MTE MIDTERM EXAM 3 FIN FINAL EXAM 4 FCG FINAL COURSE GRADE ASG * 0.30 + MTE * 0.30 + FIN * 0.40 5 RST RESIT 6 FCGR FINAL COURSE GRADE (RESIT) ASG * 0.30 + MTE * 0.30 + RST * 0.40 *** Resit Exam is Not Administered in Institutions Where Resit is not Applicable.

Further Notes About Assessment Methods

None

Assessment Criteria

To be announced.

Language of Instruction

English

Course Policies and Rules

To be announced.

Contact Details for the Lecturer(s)

mustafa.ozel@deu.edu.tr

Office Hours

Friday 9.30-11.30

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours) Lectures 13 3 39 Preparations before/after weekly lectures 13 3 39 Preparation for midterm exam 1 15 15 Preparation for final exam 1 25 25 Preparing assignments 10 5 50 Final 1 3 3 Midterm 1 3 3 TOTAL WORKLOAD (hours) 174

Contribution of Learning Outcomes to Programme Outcomes

PO/LO PO.1 PO.2 PO.3 PO.4 PO.5 PO.6 PO.7 PO.8 PO.9 PO.10 PO.11 LO.1 5 5 5 5 5 5 3 5 3 5 5 LO.2 5 5 5 5 5 5 4 5 3 5 5 LO.3 5 5 5 5 5 5 4 5 4 5 5 LO.4 5 5 5 5 5 5 2 4 3 5 5 LO.5 5 5 5 5 5 5 5 5 4 5 5 LO.6 5 5 5 5 5 5 5 5 4 5 5