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G-decompositions of matrices and related problems I

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

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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.

Item Type: Article (Journal)
Additional Information: 5537/15978
Uncontrolled Keywords: G-decomposition, G-doubly stochastic operator, Stochastic matrix, Substochastic matrix, Extreme points
Subjects: Q Science > QA Mathematics
Kulliyyahs/Centres/Divisions/Institutes (Can select more than one option. Press CONTROL button): Kulliyyah of Science > Department of Computational and Theoretical Sciences
Depositing User: Dr. Farrukh Mukhamedov
Date Deposited: 31 May 2012 11:05
Last Modified: 28 Dec 2012 14:25
URI: http://irep.iium.edu.my/id/eprint/15978

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