13D081KMF - Canonical Matrix Forms with Applications to Electrical Engineering

Course specification
Course title Canonical Matrix Forms with Applications to Electrical Engineering
Acronym 13D081KMF
Study programme Electrical Engineering and Computing
Module Applied Mathematics
Type of study doctoral studies
Lecturer (for classes)
Lecturer/Associate (for practice)
Lecturer/Associate (for OTC)
ESPB 9.0 Status elective
Condition Mathematics 1, Mathematics 2
The goal The aim of the course is to provide students with theoretical and practical knowledge on using the techniques of canonical forms to the related problems in electrical engineering. The complexity of the algorithms for calculating canonical forms (Hermite, Smith, rational and Jordan) is considered. We also discuss their application to different areas of electrical engineering.
The outcome The outcome of the course is solid mathematical support for the practical application of the canonical form on the problems in some areas of electrical engineering.
Contents
Contents of lectures Rings. Modules. Modules over a Principal ideal Domain. Normal Forms of Matrices (Hermite, Smith, Rational and Jordan). Minimal and Characteristic Polynomials. Eigenvalues and Eigenvectors. Generalized Eigenvectors. Algebraic and Geometric Multiplicities.Invariant Factors. Elementary Divisors. Systems of Linear Differential Equations. Application of canonical matrix form to electrical engineering.
Contents of exercises The practical part of teaching involves the same teaching units as theoretical contents. We will illustrated mentioned topics by the examples and by using the appropriate mathematical software.
Literature
1. J. Kečkić, Linear Algebra theory and practice, Mathematical problems and exposure 10, Naučna knjiga, Beograd, 1990.
2. D. S. Dummit, R. M. Foote, Abstract Algebra, third edition, Johan Wiley & Sons, Hoboken, 2004.
3. F. P. Gantmaher, Theory of Matrices, Nauka, Moscow, 1988.
4. S. Weintraub, Jordan Canonical Form: Application to Differential Equations, Morgan and Claypool, 2008.
5. S. Weintraub, Jordan Canonical Form: Theory and Practice, Morgan and Claypool 2009.
Number of hours per week during the semester/trimester/year
Lectures Exercises OTC Study and Research Other classes
6
Methods of teaching Formal lecture, practicals ang group work.
Knowledge score (maximum points 100)
Pre obligations Points Final exam Points
Activites during lectures 25 Test paper 50
Practical lessons Oral examination
Projects
Colloquia 25
Seminars