G-decompositions of matrices and related problems i

Rasul Ganikhodzhaev, Farrukh Mukhamedov, Mansoor Saburov

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)1344-1366
Number of pages23
JournalLinear Algebra and Its Applications
Issue number5
Publication statusPublished - Mar 1 2012
Externally publishedYes


  • Extreme points
  • G-decomposition
  • G-doubly stochastic operator
  • Stochastic matrix
  • Substochastic matrix

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics


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