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Special Sessions in Applications of Computer Algebra

ACA 2015: Applications of Computer Algebra pp 119–136Cite as

Finding Eigenvalues of Self-maps with the Kronecker Canonical Form

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Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 198))

Abstract

Recent research has examined how to study the topological features of a continuous self-map by means of the persistence of the eigenspaces, for given eigenvalues, of the endomorphism induced in homology over a field. This raised the question of how to select dynamically significant eigenvalues. The present paper aims to answer this question, giving an algorithm that computes the persistence of eigenspaces for every eigenvalue simultaneously, also expressing said eigenspaces as direct sums of “finite” and “singular” subspaces.

This research is supported by the Toposys project FP7-ICT-318493-STREP, by the Polish MNiSzW grant Nr 2621/7.PR/12/2013/2, and by the National Science Centre (Poland) grant DEC-2013/09/N/ST6/02995

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References

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Author information

Authors and Affiliations

  1. Division of Computational Mathematics, Faculty of Mathematics and Computer Science, Jagiellonian University, Kraków, Poland

    Marc Ethier, Grzegorz Jabłoński & Marian Mrozek

  2. University of Saint-Boniface, Winnipeg, MB, Canada

    Marc Ethier

  3. Institute of Science and Technology Austria, Klosterneuburg, Austria

    Grzegorz Jabłoński

Authors
  1. Marc Ethier
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  2. Grzegorz Jabłoński
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  3. Marian Mrozek
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Corresponding author

Correspondence to Marc Ethier .

Editor information

Editors and Affiliations

  1. Department of Physics and Computer Science, Wilfrid Laurier University, Waterloo, Ontario, Canada

    Ilias S. Kotsireas

  2. Institute of Mathematics, University of Valladolid, Valladolid, Spain

    Edgar Martínez-Moro

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Ethier, M., Jabłoński, G., Mrozek, M. (2017). Finding Eigenvalues of Self-maps with the Kronecker Canonical Form. In: Kotsireas, I., Martínez-Moro, E. (eds) Applications of Computer Algebra. ACA 2015. Springer Proceedings in Mathematics & Statistics, vol 198. Springer, Cham. https://doi.org/10.1007/978-3-319-56932-1_8

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