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Bulletin of the Iranian Mathematical Society

, Volume 45, Issue 5, pp 1457–1466 | Cite as

Generalized Doubly Stochastic Matrices and Linear Preservers of D-majorization

  • Ahmad MohammadhasaniEmail author
Original Paper
  • 31 Downloads

Abstract

D-majorization is a group-induced cone ordering on \({\mathbb {R}}^{n}\) induced by group \(G=\{cP: c\in \{-1,1\},\ \ P\in {\mathcal {P}}(n)\}\), where \({\mathcal {P}}(n)\) is the set of all n-by-n permutation matrices. For x, \(y\in {\mathbb {R}}^{n}\), x is said to be D-majorized by y (denoted by \(x\prec _{D}y\)) if there exists some \(D\in \mathrm{Conv(G)}\) such that \(x=Dy\). In the present paper, the concept of D-majorization is studied and then the linear preservers of this concept are characterized.

Keywords

D-majorization Generalized doubly stochastic matrix Linear preserver 

Mathematics Subject Classification

Primary 15A04 Secondary 15A51 

Notes

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Copyright information

© Iranian Mathematical Society 2019

Authors and Affiliations

  1. 1.Department of Mathematics and Computer SciencesSirjan University of TechnologySirjanIran

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