G-decompositions of matrices and related problems I
In the present paper we introduce a notion of G-decompositions of matrices. Main result of the paper is that a symmetric matrix Am has a G-decomposition in the class of stochastic (resp. substochastic) matrices if and only if Am belongs to the set Um (resp. Um). To prove the main result, we study ex...
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| Format: | Article |
| Language: | English |
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Elsevier Science Inc
2012
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| Online Access: | http://irep.iium.edu.my/15978/ http://irep.iium.edu.my/15978/1/mfgrms-LAA%282012%29.pdf |
| _version_ | 1848777864508342272 |
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| author | Ganikhodzhaev, Rasul Mukhamedov, Farrukh Saburov, Mansoor |
| author_facet | Ganikhodzhaev, Rasul Mukhamedov, Farrukh Saburov, Mansoor |
| author_sort | Ganikhodzhaev, Rasul |
| building | IIUM Repository |
| collection | Online Access |
| description | In the present paper we introduce a notion of G-decompositions of matrices. Main result of the paper is that a symmetric matrix Am has a G-decomposition in the class of stochastic (resp. substochastic) matrices if and only if Am belongs to the set Um (resp. Um). To prove the main result, we study extremal points and geometrical structures of the sets Um, Um. Note that such kind of investigations enables to study Birkhoff’s problem for quadratic G-doubly stochastic operators. |
| first_indexed | 2025-11-14T14:52:46Z |
| format | Article |
| id | iium-15978 |
| institution | International Islamic University Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T14:52:46Z |
| publishDate | 2012 |
| publisher | Elsevier Science Inc |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | iium-159782012-12-28T06:25:15Z http://irep.iium.edu.my/15978/ G-decompositions of matrices and related problems I Ganikhodzhaev, Rasul Mukhamedov, Farrukh Saburov, Mansoor QA Mathematics In the present paper we introduce a notion of G-decompositions of matrices. Main result of the paper is that a symmetric matrix Am has a G-decomposition in the class of stochastic (resp. substochastic) matrices if and only if Am belongs to the set Um (resp. Um). To prove the main result, we study extremal points and geometrical structures of the sets Um, Um. Note that such kind of investigations enables to study Birkhoff’s problem for quadratic G-doubly stochastic operators. Elsevier Science Inc 2012-03-01 Article PeerReviewed application/pdf en http://irep.iium.edu.my/15978/1/mfgrms-LAA%282012%29.pdf Ganikhodzhaev, Rasul and Mukhamedov, Farrukh and Saburov, Mansoor (2012) G-decompositions of matrices and related problems I. Linear Algebra and its Applications, 436 (5). pp. 1344-1366. ISSN 0024-3795 http://dx.doi.org/10.1016/j.laa.2011.08.012 10.1016/j.laa.2011.08.012 |
| spellingShingle | QA Mathematics Ganikhodzhaev, Rasul Mukhamedov, Farrukh Saburov, Mansoor G-decompositions of matrices and related problems I |
| title | G-decompositions of matrices and related problems I |
| title_full | G-decompositions of matrices and related problems I |
| title_fullStr | G-decompositions of matrices and related problems I |
| title_full_unstemmed | G-decompositions of matrices and related problems I |
| title_short | G-decompositions of matrices and related problems I |
| title_sort | g-decompositions of matrices and related problems i |
| topic | QA Mathematics |
| url | http://irep.iium.edu.my/15978/ http://irep.iium.edu.my/15978/ http://irep.iium.edu.my/15978/ http://irep.iium.edu.my/15978/1/mfgrms-LAA%282012%29.pdf |