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On Multiple Eigenvalues of a Matrix Dependent on a Parameter

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Computer Algebra in Scientific Computing (CASC 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9890))

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Abstract

In this paper, a square matrix with elements linearly dependent on a parameter is considered. We propose an algorithm to find all the values of the parameter such that the matrix has a multiple eigenvalue. We construct a polynomial whose roots are these values of the parameter. A numerical example shows how the algorithm works.

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Acknowledgments

The author is grateful to the anonymous referees for valuable suggestions that helped to improve the paper.

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Authors and Affiliations

  1. Saint-Petersburg State University, Saint-Petersburg, Russia

    Elizabeth A. Kalinina

Authors
  1. Elizabeth A. Kalinina
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Correspondence to Elizabeth A. Kalinina .

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Editors and Affiliations

  1. Laboratory of Information Technologies, Joint Institute of Nuclear Research, Dubna, Russia

    Vladimir P. Gerdt

  2. Institut für Mathematik, Universität Kassel, Kassel, Germany

    Wolfram Koepf

  3. Institut für Mathematik, Universität Kassel, Kassel, Germany

    Werner M. Seiler

  4. Institute of Theoretical and Applied Mechanics, Russian Academy of Sciences, Novosibirsk, Russia

    Evgenii V. Vorozhtsov

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Kalinina, E.A. (2016). On Multiple Eigenvalues of a Matrix Dependent on a Parameter. In: Gerdt, V., Koepf, W., Seiler, W., Vorozhtsov, E. (eds) Computer Algebra in Scientific Computing. CASC 2016. Lecture Notes in Computer Science(), vol 9890. Springer, Cham. https://doi.org/10.1007/978-3-319-45641-6_20

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  • DOI: https://doi.org/10.1007/978-3-319-45641-6_20

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-45640-9

  • Online ISBN: 978-3-319-45641-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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