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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| Дата: | 2018 |
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| Формат: | Стаття |
| Мова: | English |
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Lugansk National Taras Shevchenko University
2018
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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/915 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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oai:ojs.admjournal.luguniv.edu.ua: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 |
| 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 |
2024-04-12T06:25:29Z |
| last_indexed |
2024-04-12T06:25:29Z |
| _version_ |
1796109224494759936 |