$G-$Decompositions of Matrices and Related Problems I
| Autor: | Ganikhodjaev, Rasul, Mukhamedov, Farrukh, Saburov, Mansoor |
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| Rok vydání: | 2010 |
| Předmět: | |
| Zdroj: | Linear Algebra and its Applications 436 (2012) 1344--1366 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.laa.2011.08.012 |
| Popis: | In the present paper we introduce a notion of $G-$decompositions of matrices. Main result of the paper is that a symmetric matrix $A_m$ has a $G-$decomposition in the class of stochastic (resp. substochastic) matrices if and only if $A_m$ belongs to the set ${\mathbf{U}}^m$ (resp. ${\mathbf{U}}_m$). To prove the main result, we study extremal points and geometrical structures of the sets ${\mathbf{U}}^m$, ${\mathbf{U}}_m$. Note that such kind of investigations enables to study Birkhoff's problem for quadratic $G-$doubly stochastic operators. Comment: 23 pages |
| Databáze: | arXiv |
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