Skip to main content
Log in

Linear Operators Preserving and Converting Majorizations of the (0, 1)-Vectors

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

The paper investigates and characterizes linear operators preserving weak majorization of the (0, 1)-vectors and linear operators converting vector majorization of the (0, 1)-vectors to weak majorization.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

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

    Article  MathSciNet  MATH  Google Scholar 

  2. L. B. Beasley, S.-G. Lee, and Y.-H. Lee, “A characterization of strong preservers of matrix majorization,” Linear Algebra Appl., 367, 341–346 (2003).

    Article  MathSciNet  MATH  Google Scholar 

  3. L. B. Beasley and S.-G. Lee, “Linear operators preserving multivariate majorization,” Linear Algebra Appl., 304, No. 1, 141–159 (2000).

    Article  MathSciNet  MATH  Google Scholar 

  4. G. Dahl, “Matrix majorization,” Linear Algebra Appl., 288, 53–73 (1999).

    Article  MathSciNet  MATH  Google Scholar 

  5. G. Dahl, A. Guterman, and P. Shteyner, “Majorization for matrix classes,” Linear Algebra Appl., 555, 201–221 (2018).

    Article  MathSciNet  MATH  Google Scholar 

  6. G. Dahl, A. Guterman, and P. Shteyner, “Majorization for (0,1)-matrices,” Linear Algebra Appl., 585, 147–163 (2020).

    Article  MathSciNet  MATH  Google Scholar 

  7. J. Dieudonné, “Sur une g´en´eralisation du groupe orthogonal `a quatre variables,” Arch. Math., 1, 282–287 (1949).

    Article  MathSciNet  MATH  Google Scholar 

  8. G. Frobenius, “Uber die Darstellung der endlichen Gruppen durch linear Substitutionen,” Sitz. Deutsch. Akad. Wiss. Berlin, 994–1015 (1897).

  9. A. Guterman and P. M. Shteyner, “Linear operators preserving majorization of matrix tuples,” Vestn. St. Petersburg Univ., Ser. Mat., 7(65), 217–229 (2020).

    MATH  Google Scholar 

  10. A. Guterman and P. Shteyner, “Linear converters of weak, directional and strong majorizations,” Linear Algebra Appl., 613, 340–346 (2021).

    Article  MathSciNet  MATH  Google Scholar 

  11. A. Guterman and P. Shteyner, “Linear operators preserving strong majorization of (0,1)-matrices,” Linear Algebra Appl., 658, 116–150 (2023).

    Article  MathSciNet  MATH  Google Scholar 

  12. A. M. Hasani and M. Radjabalipour, “Linear preserver of matrix majorization,” Int. J. Pure Appl. Math., 32(4), 475–482 (2006).

    MathSciNet  MATH  Google Scholar 

  13. C.-K. Li and S. Pierce, “Linear preserver problems,” Amer. Math. Monthly, 108, No. 7, 591–605 (2001).

    Article  MathSciNet  MATH  Google Scholar 

  14. C.-K. Li and E. Poon, “Linear operators preserving directional majorization,” Linear Algebra Appl., 325, No. 1, 141–146 (2001).

    Article  MathSciNet  MATH  Google Scholar 

  15. A. W. Marshall, I. Olkin, and B. C. Arnold, Inequalities: Theory of Majorization and Its Applications, second edition, Springer, New York (2011).

  16. F. D. Martínez Pería, P. G. Massey, and L. E. Silvestre, “Weak matrix majorization,” Linear Algebra Appl., 403, 343–368 (2005).

    Article  MathSciNet  MATH  Google Scholar 

  17. S. Pierce et al, “A survey of linear preserver problems,” Linear Multilinear Algebra, 33, Nos. 1–2, 1–119 (1992).

    MathSciNet  Google Scholar 

  18. I. Schur, Einige Bemerkungen zur Determinantentheorie, Akad. Wiss., Berlin, 454–463 (1925).

    MATH  Google Scholar 

  19. P. Shteyner, “Converting column majorization,” Zap. Nauchn. Semin. POMI, 496, 195–215 (2020); English transl., J. Math. Sci., 255, No. 3, 340–352 (2021).

  20. P. Shteyner, “Linear operators preserving combinatorial matrix sets,” Zap. Nauchn. Semin. POMI, 504, 181–199 (2021); English transl., J. Math. Sci., 262, No. 1, 114–125 (2022).

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to P. M. Shteyner.

Additional information

Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 514, 2022, pp. 204–220.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Shteyner, P.M. Linear Operators Preserving and Converting Majorizations of the (0, 1)-Vectors. J Math Sci 272, 615–624 (2023). https://doi.org/10.1007/s10958-023-06454-6

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10958-023-06454-6

Navigation