Vestnik Sankt-Peterburgskogo Universiteta. Seriya 10. Prikladnaya Matematika. Informatika. Protsessy Upravleniya
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Vestnik S.-Petersburg Univ. Ser. 10. Prikl. Mat. Inform. Prots. Upr.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Vestnik S.-Petersburg Univ. Ser. 10. Prikl. Mat. Inform. Prots. Upr., 2016, Issue 2, Pages 26–32 (Mi vspui287)  

Applied mathematics

Repeated eigenvalues of a matrix with elements polynomially dependent on a parameter

E. A. Kalinina

St. Petersburg State University, 7–9, Universitetskaya nab., St. Petersburg, 199034, Russian Federation

Abstract: Earlier matrices with multiple eigenvalues were considered only for theoretical purposes. However, now such non-generic matrices are also of practical interest because they appear in different problems of quantum mechanics, nuclear physics, optics and dynamic of mechanical systems. A square matrix with elements that are linearly dependent on a parameter is considered in this paper. A method to find the values of the parameter such that the matrix has a repeated eigenvalue is considered. We find the polynomial whose roots are these values of the parameter using only finite number of algebraic operations on the matrix elements. The method can be generalized to matrices with elements algebraically dependent on a parameter. A numerical example of how to find the required parameter values is considered. Refs 16.

Keywords: the Kronecker product, the Leverrier method, the Newton sums.

DOI: https://doi.org/10.21638/11701/spbu10.2016.203

Full text: PDF file (223 kB)
References: PDF file   HTML file

UDC: 512.643
Received: December 10, 2015
Accepted: February 25, 2016

Citation: E. A. Kalinina, “Repeated eigenvalues of a matrix with elements polynomially dependent on a parameter”, Vestnik S.-Petersburg Univ. Ser. 10. Prikl. Mat. Inform. Prots. Upr., 2016, no. 2, 26–32

Citation in format AMSBIB
\Bibitem{Kal16}
\by E.~A.~Kalinina
\paper Repeated eigenvalues of a matrix with elements polynomially dependent on a parameter
\jour Vestnik S.-Petersburg Univ. Ser. 10. Prikl. Mat. Inform. Prots. Upr.
\yr 2016
\issue 2
\pages 26--32
\mathnet{http://mi.mathnet.ru/vspui287}
\crossref{https://doi.org/10.21638/11701/spbu10.2016.203}
\elib{https://elibrary.ru/item.asp?id=26415556}


Linking options:
  • http://mi.mathnet.ru/eng/vspui287
  • http://mi.mathnet.ru/eng/vspui/y2016/i2/p26

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Вестник Санкт-Петербургского университета. Серия 10. Прикладная математика. Информатика. Процессы управления
    Number of views:
    This page:99
    Full text:16
    References:13
    First page:5

     
    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2022