TY - JOUR

T1 - Neighborhood radius estimation for Arnold's miniversal deformations of complex and p-adic matrices

AU - Bovdi, Victor A.

AU - Salim, Mohammed A.

AU - Sergeichuk, Vladimir V.

N1 - Funding Information:
This research was supported in part by the UAEU Program for Advanced Research , grant G00001922 , and by the UAEU Research Start-up Competition , grant G00001889 . The authors would like to thank the referees for their constructive comments, which helped us to improve the manuscript.
Publisher Copyright:
© 2016 Elsevier Inc.

PY - 2017/1/1

Y1 - 2017/1/1

N2 - V.I. Arnold (1971) constructed a simple normal form to which all complex matrices B in a neighborhood U of a given square matrix A can be reduced by similarity transformations that smoothly depend on the entries of B. We calculate the radius of the neighborhood U. A.A. Mailybaev (1999, 2001) constructed a reducing similarity transformation in the form of Taylor series; we construct this transformation by another method. We extend Arnold's normal form to matrices over the field Qp of p-adic numbers and the field F((T)) of Laurent series over a field F.

AB - V.I. Arnold (1971) constructed a simple normal form to which all complex matrices B in a neighborhood U of a given square matrix A can be reduced by similarity transformations that smoothly depend on the entries of B. We calculate the radius of the neighborhood U. A.A. Mailybaev (1999, 2001) constructed a reducing similarity transformation in the form of Taylor series; we construct this transformation by another method. We extend Arnold's normal form to matrices over the field Qp of p-adic numbers and the field F((T)) of Laurent series over a field F.

KW - Matrices over p-adic numbers

KW - Miniversal deformations

KW - Reducing transformations

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U2 - 10.1016/j.laa.2016.09.026

DO - 10.1016/j.laa.2016.09.026

M3 - Article

AN - SCOPUS:84988947026

SN - 0024-3795

VL - 512

SP - 97

EP - 112

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -