D-stratification and hierarchy graphs of the space of order 2 and 3 matrix pencils
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Cita com:
hdl:2117/131164
Tipus de documentArticle
Data publicació2019
EditorUniversal journal of mathematics and applications
Condicions d'accésAccés obert
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Reconeixement-NoComercial-SenseObraDerivada 3.0 Espanya
Abstract
Small changes in the entries of a matrix pencil may lead to important changes in its Kronecker normal form. Studies about the effect of small perturbations have been made when considering the stratification associated with the strict equivalence between matrix pencils. In this work, we consider a partition in the space of pairs of matrices associated to regular matrix pencils, which will be proved to be a finite stratification of the space of such matrix pencils, called D-stratification. Matrix pencils in the same strata are those having some prescribed Segre indices. We study the effect of perturbations which lead to changes in the Kronecker canonical form, preserving the order of the nilpotent part. Our goal is to determine which DD-strata can be reached. In the cases where the order of the matrix pencils is 2 or 3, we obtain the corresponding hierarchy graphs, illustrating the DD-strata that can be reached when applying some small perturbations
CitacióGarcia-Planas, M.I.; Magret, M. D. D-stratification and hierarchy graphs of the space of order 2 and 3 matrix pencils. "Universal journal of mathematics and applications", 2019, vol. 2, núm. 1, p. 14-23.
ISSN2619-9653
Versió de l'editorhttp://dergipark.gov.tr/ujma/issue/44032/454890
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