Software for reducing a matrix to Arnold’s normal form by smooth similarity transformations

Abstract

V.I.Arnold (1971) constructed a miniversal deformation of each Jordan matrix $J$; that is, a simple normal form to which all matrices $A$ close to $J$ can be reduced by similarity transformations that smoothly depend on the entries of $A$. We describe a software for reducing a matrix in an neighborhood of $J$ to Arnold's normal form by smooth similarity transformations and calculating the transforming matrix.