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 -