Courses – Fakultet tehničkih nauka u Novom Sadu

Subject: Eigenvalues and eigenvectors (17.DOM63L)

Type of studies	Title
Doctoral Academic Studies	Mathematics in Engineering (Year: 1, Semester: Summer)

General information:

Category	Scientific-professional
Scientific or art field	Teorijska i primenjena matematika
ECTS	10

Acquiring basic knowledge in the field of Eigenvalues and eigenvectors and its application in the analysis of dynamic systems and in engineering. The aim of this course is to develop a special way of thinking by using principles of the applied linear algebra where Eigenvalues and eigenvectors have a very important role. The knowledge they gain is a basis for a better understanding other professional courses and for a successful continuation in studies.

Understanding concepts of characteristic roots and vectors. Theoretical knowledge of Eigenvalues and eigenvectors, which has a great application in engineering. Knowledge they have acquired, students learn to apply methods for finding Eigenvalues and eigenvectors and to choose algorithms for solving future problems in professional field.

Localization of eigenvalues of the Gershgrino type theorems. Localization of eigenvalues of stochastic matrices. Algorithms for calculating eigenvalues - symmetric matrices and asymmetric matrices. Pseudospectrum. Analysis of stability of dynamic systems. Generalized eigenvalues . Matrix polynomials. Applications in Engineering.

The presentation of the theoretical part during the lecture classes is followed by the characteristic examples which contribute to better understanding of the subject matter. The students are expected to individually study the additional literature which they discuss with the . subject teacher atthe consultation classes. Through research and study work the student will, on the bases of scientific journals and other literature, develop further understanding of the material covered in lectures. Working with the course teacher the student develops the ability to independently work on a scientific paper.

Authors	Title	Year	Publisher	Language
L. Hogben	Handbook of Linear Algebra	2007	CRC Press	English
S.K. Godunov	Modern Aspects of Linear Algebra. Translations of Mathematical Monographs	1997	American Mathematical Society	English
R. S. Varga	Geršgorin and His Circles	2004	Springer	English
N. Trefethen, M. Embree	Spectra and Pseudospectra. The Behaviour of Nonnormal Matrices and Operators	2005	Princeton University Press	English
J.W. Demmel	Applied Numerical Linear Algebra	1997	SIAM	English
G. Golub, C.F. Van Loan	Matrix Computation	1996	Johns Hopkins Univ Pr., 3rd edition	English