Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4598397 | Linear Algebra and its Applications | 2017 | 16 Pages |
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 QpQp of p -adic numbers and the field F((T))F((T)) of Laurent series over a field FF.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Victor A. Bovdi, Mohammed A. Salim, Vladimir V. Sergeichuk,