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 language | English |
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Pages (from-to) | 97-112 |
Number of pages | 16 |
Journal | Linear Algebra and Its Applications |
Volume | 512 |
DOIs | |
Publication status | Published - 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