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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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Main Authors: Ganikhodzhaev, Rasul, Mukhamedov, Farrukh, Saburov, Mansoor
Format: Article
Language:English
Published: Elsevier Science Inc 2012
Subjects:
QA Mathematics
Online Access:http://irep.iium.edu.my/15978/1/mfgrms-LAA%282012%29.pdf
http://irep.iium.edu.my/15978/
http://dx.doi.org/10.1016/j.laa.2011.08.012
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spelling my.iium.irep.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 REM 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
institution Universiti Islam Antarabangsa Malaysia
building IIUM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider International Islamic University Malaysia
content_source IIUM Repository (IREP)
url_provider http://irep.iium.edu.my/
language English
topic QA Mathematics
spellingShingle QA Mathematics
Ganikhodzhaev, Rasul
Mukhamedov, Farrukh
Saburov, Mansoor
G-decompositions of matrices and related problems I
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.
format Article
author Ganikhodzhaev, Rasul
Mukhamedov, Farrukh
Saburov, Mansoor
author_facet Ganikhodzhaev, Rasul
Mukhamedov, Farrukh
Saburov, Mansoor
author_sort Ganikhodzhaev, Rasul
title G-decompositions of matrices and related problems I
title_short 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_sort g-decompositions of matrices and related problems i
publisher Elsevier Science Inc
publishDate 2012
url http://irep.iium.edu.my/15978/1/mfgrms-LAA%282012%29.pdf
http://irep.iium.edu.my/15978/
http://dx.doi.org/10.1016/j.laa.2011.08.012
_version_ 1643607079379795968
score 13.18916

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