Miniversal deformations of matrices of bilinear forms

被引：19

作者：

Dmytryshyn, Andrii R. ^{[2
,3
]}

Futorny, Vyacheslav ^{[4
]}

Sergeichuk, Vladimir V. ^{[1
]}

机构：

[1] Ukrainian Acad Sci, Inst Math, Kiev, Ukraine

[2] Umea Univ, Dept Comp Sci, SE-90187 Umea, Sweden

[3] Ukrainian Acad Sci, HPC2N, Kiev, Ukraine

[4] Univ Sao Paulo, Dept Math, BR-05508 Sao Paulo, Brazil

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2012年 / 436卷 / 07期

基金：

巴西圣保罗研究基金会;

关键词：

Bilinear forms; Miniversal deformations; VERSAL DEFORMATIONS; SESQUILINEAR FORMS; JORDAN ALGEBRAS; PENCILS; FAMILIES; TRANSFORMATION; ELEMENTS;

D O I：

10.1016/j.laa.2011.11.010

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Arnold [V.I. Arnold, On matrices depending on parameters, Russian Math. Surveys 26 (2) (1971) 29-43] constructed miniversal deformations of square complex matrices under similarity; that is, a simple normal form to which not only a given square matrix A but all matrices B close to it can be reduced by similarity transformations that smoothly depend on the entries of B. We construct miniversal deformations of matrices under congruence. (C) 2011 Elsevier Inc. All rights reserved.

引用

页码：2670 / 2700

页数：31

共 50 条

[1] ON MINIVERSAL DEFORMATIONS OF MATRICES
KASHCHENKO, SA
[J]. RUSSIAN MATHEMATICAL SURVEYS, 1988, 43 (01) : 241 - 242
[2] Miniversal deformations of marked matrices
Compta, A
Ferrer, J
Puerta, F
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2003, 361 : 181 - 201
[3] Miniversal deformations of matrices under *congruence and reducing transformations
Dmytryshyn, Andrii
Futorny, Vyacheslav
Sergeichuk, Vladimir V.
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2014, 446 : 388 - 420
[4] Miniversal deformations of pairs of symmetric matrices under congruence
Dmytryshyn, Andrii
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2019, 568 : 84 - 105
[5] MINIVERSAL DEFORMATIONS OF DIALGEBRAS
Fialowski, Alice
Majumdar, Anita
[J]. COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 2009, 11 (03) : 413 - 432
[6] Miniversal deformations of pairs of skew-symmetric matrices under congruence
Dmytryshyn, Andrii
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2016, 506 : 506 - 534
[7] Simplest miniversal deformations of matrices, matrix pencils, and contragredient matrix pencils
García-Planas, MI
Sergeichuk, VV
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 1999, 303 : 45 - 61
[8] Theorems on matrices and bilinear forms
Bromwich, TJI
[J]. PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 1902, 11 : 75 - 89
[9] Miniversal deformations of observable markedmatrices
Compta, Albert
Ferrer, Josep
Pena, Marta
[J]. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2014, 37 (01) : 20 - 31
[10] Examples of miniversal deformations of infinity algebras
Fialowski, Alice
Penkava, Michael
[J]. FORUM MATHEMATICUM, 2007, 19 (03) : 463 - 486

← 1 2 3 4 5 →