Miniversal deformations of chains of linear mappings

V.I.Arnold [Russian Math. Surveys, 26 (no. 2), 1971, pp. 29-43] gave a miniversal deformation of matrices of linear operators; that is, a simple canonical form, to which not only a given square matrix \(A\), but also the family of all matrices close to \(A\), can be reduced by similarity transformat...

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Date:2018
Main Authors: Gaiduk, T. N., Sergeichuk, V. V., Zharko, N. A.
Format: Article
Language:English
Published: Lugansk National Taras Shevchenko University 2018
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Online Access:https://admjournal.luguniv.edu.ua/index.php/adm/article/view/915
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Journal Title:Algebra and Discrete Mathematics

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Algebra and Discrete Mathematics
id admjournalluguniveduua-article-915
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spelling admjournalluguniveduua-article-9152018-03-21T07:18:38Z Miniversal deformations of chains of linear mappings Gaiduk, T. N. Sergeichuk, V. V. Zharko, N. A. Parametric matrices; Quivers; Miniversal deformations 15A21; 16G20 V.I.Arnold [Russian Math. Surveys, 26 (no. 2), 1971, pp. 29-43] gave a miniversal deformation of matrices of linear operators; that is, a simple canonical form, to which not only a given square matrix \(A\), but also the family of all matrices close to \(A\), can be reduced by similarity transformations smoothly depending on the entries of matrices. We study miniversal deformations of quiver representations and obtain a miniversal deformation of matrices of chains of linear mappings \[ V_1 \,\frac{}{\qquad}\, V_2\,\frac{}{\qquad}\, \cdots \,\frac{}{\qquad}\, V_t\,, \] where all \(V_i\) are complex or real vector spaces and each line denotes \(\longrightarrow\) or \(\longleftarrow\). Lugansk National Taras Shevchenko University 2018-03-21 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/915 Algebra and Discrete Mathematics; Vol 4, No 1 (2005) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/915/444 Copyright (c) 2018 Algebra and Discrete Mathematics
institution Algebra and Discrete Mathematics
baseUrl_str
datestamp_date 2018-03-21T07:18:38Z
collection OJS
language English
topic Parametric matrices
Quivers
Miniversal deformations
15A21
16G20
spellingShingle Parametric matrices
Quivers
Miniversal deformations
15A21
16G20
Gaiduk, T. N.
Sergeichuk, V. V.
Zharko, N. A.
Miniversal deformations of chains of linear mappings
topic_facet Parametric matrices
Quivers
Miniversal deformations
15A21
16G20
format Article
author Gaiduk, T. N.
Sergeichuk, V. V.
Zharko, N. A.
author_facet Gaiduk, T. N.
Sergeichuk, V. V.
Zharko, N. A.
author_sort Gaiduk, T. N.
title Miniversal deformations of chains of linear mappings
title_short Miniversal deformations of chains of linear mappings
title_full Miniversal deformations of chains of linear mappings
title_fullStr Miniversal deformations of chains of linear mappings
title_full_unstemmed Miniversal deformations of chains of linear mappings
title_sort miniversal deformations of chains of linear mappings
description V.I.Arnold [Russian Math. Surveys, 26 (no. 2), 1971, pp. 29-43] gave a miniversal deformation of matrices of linear operators; that is, a simple canonical form, to which not only a given square matrix \(A\), but also the family of all matrices close to \(A\), can be reduced by similarity transformations smoothly depending on the entries of matrices. We study miniversal deformations of quiver representations and obtain a miniversal deformation of matrices of chains of linear mappings \[ V_1 \,\frac{}{\qquad}\, V_2\,\frac{}{\qquad}\, \cdots \,\frac{}{\qquad}\, V_t\,, \] where all \(V_i\) are complex or real vector spaces and each line denotes \(\longrightarrow\) or \(\longleftarrow\).
publisher Lugansk National Taras Shevchenko University
publishDate 2018
url https://admjournal.luguniv.edu.ua/index.php/adm/article/view/915
work_keys_str_mv AT gaiduktn miniversaldeformationsofchainsoflinearmappings
AT sergeichukvv miniversaldeformationsofchainsoflinearmappings
AT zharkona miniversaldeformationsofchainsoflinearmappings
first_indexed 2025-12-02T15:45:15Z
last_indexed 2025-12-02T15:45:15Z
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