ACA 2015: Applications of Computer Algebra pp 119-136 | Cite as
Finding Eigenvalues of Self-maps with the Kronecker Canonical Form
Conference paper
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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 formReferences
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