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

Victor A. Bovdi, Mohammed A. Salim, Vladimir V. Sergeichuk

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)97-112
Number of pages16
JournalLinear Algebra and Its Applications
Volume512
DOIs
Publication statusPublished - Jan 1 2017

Keywords

  • Matrices over p-adic numbers
  • Miniversal deformations
  • Reducing transformations

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics

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