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Finding Eigenvalues of Self-maps with the Kronecker Canonical Form

  • Marc EthierEmail author
  • Grzegorz Jabłoński
  • Marian Mrozek
Conference paper
  • 601 Downloads
Part of the Springer Proceedings in Mathematics & Statistics book series (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.

Keywords

Computational topology Persistent homology Self-maps Matrix pencils Kronecker canonical form 

References

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Marc Ethier
    • 1
    • 2
    Email author
  • Grzegorz Jabłoński
    • 1
    • 3
  • Marian Mrozek
    • 1
  1. 1.Division of Computational Mathematics, Faculty of Mathematics and Computer ScienceJagiellonian UniversityKrakówPoland
  2. 2.University of Saint-BonifaceWinnipegCanada
  3. 3.Institute of Science and Technology AustriaKlosterneuburgAustria

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