Skip to main content
SpringerLink
Log in

Generalized Doubly Stochastic Matrices and Linear Preservers of D-majorization

  • Original Paper
  • Published:
Bulletin of the Iranian Mathematical Society Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Ando, T.: Majorization, doubly stochastic matrices, and comparision of eigenvalues. Linear Algebra Appl. 118, 163–248 (1989)

    Article  MathSciNet  Google Scholar 

  2. Giovagnoli, A., Wynn, H.P.: G-majorization with applications to matrix orderings. Linear Algebra Appl. 67, 111–135 (1985)

    Article  MathSciNet  Google Scholar 

  3. Hadian Nadoshan, M.A., Armandnejad, A.: \(B\)-majorization and its linear preservers. Linear Algebra Appl. 178, 218–227 (2013)

    MathSciNet  MATH  Google Scholar 

  4. Li, C.K., Poon, E.: Linear operators preservering directional majorization. Linear Algebra Appl. 325, 141–146 (2001)

    Article  MathSciNet  Google Scholar 

  5. Mohammadhasani, A., Radjabalipour, M.: On linear preservers of (right) matrix majorization. Linear Algebra Appl. 423, 255–261 (2007)

    Article  MathSciNet  Google Scholar 

  6. Niezgoda, M.: Cone orderings, group majorizations and similarly separable vectors. Linear Algebra Appl. 436, 579–594 (2012)

    Article  MathSciNet  Google Scholar 

  7. Marshall, A.W., Olkin, I., Arnold, B.C.: Inequalities: Theory of Majorization and its Applications. Springer, New York (2011)

    Book  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Computer Sciences, Sirjan University of Technology, Sirjan, Iran

    Ahmad Mohammadhasani

Authors
  1. Ahmad Mohammadhasani
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ahmad Mohammadhasani.

Additional information

Communicated by Hamid Reza Ebrahimi Vishki.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Mohammadhasani, A. Generalized Doubly Stochastic Matrices and Linear Preservers of D-majorization. Bull. Iran. Math. Soc. 45, 1457–1466 (2019). https://doi.org/10.1007/s41980-019-00208-4

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s41980-019-00208-4

Keywords

Mathematics Subject Classification

Search

Navigation