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

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• 作者：Victor A. Bovdi^a ; ^{vbovdi@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; Mohammed A. Salim^a ; ^{msalim@uaeu.ac.ae" class="auth_mail" title="E-mail the corresponding author} ; Vladimir V. Sergeichuk^b ; ^{sergeich@imath.kiev.ua" class="auth_mail" title="E-mail the corresponding author}
• 关键词：15A21 ; 15B33 ; 37J40
• 刊名：Linear Algebra and its Applications
• 出版年：2017
• 出版时间：1 January 2017
• 年：2017
• 卷：512
• 期：Complete
• 页码：97-112
• 全文大小：357 K

文摘

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 g" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0024379516304256&_mathId=si1.gif&_user=111111111&_pii=S0024379516304256&_rdoc=1&_issn=00243795&md5=fad62d3e1f0cb8e876b101f46ae96004" title="Click to view the MathML source">Q_pgif" overflow="scroll">Qp of p  -adic numbers and the field g" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0024379516304256&_mathId=si2.gif&_user=111111111&_pii=S0024379516304256&_rdoc=1&_issn=00243795&md5=5f22dead8ef63b0de358ded7dbce092d" title="Click to view the MathML source">F((T))gif" overflow="scroll">F((T)) of Laurent series over a field g" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0024379516304256&_mathId=si106.gif&_user=111111111&_pii=S0024379516304256&_rdoc=1&_issn=00243795&md5=e16f185adb96f05eb2858c8056f10508" title="Click to view the MathML source">Fgif" overflow="scroll">F.