{"paper":{"title":"Neighborhood radius estimation for Arnold's miniversal deformations of complex and $p$-adic matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.RA","authors_text":"Mohammed A. Salim, Victor A. Bovdi, Vladimir V. Sergeichuk","submitted_at":"2016-11-11T01:17:02Z","abstract_excerpt":"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 $\\mathbb Q_p$ of $p$-adic numbers and the field $\\mathbb F((T))$ of Laurent series over a field $\\mathbb F$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.03557","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}