Linear operators preserving and converting majorizations of $(0, 1)$-vectors
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXXV, Tome 514 (2022), pp. 204-220 Cet article a éte moissonné depuis la source Math-Net.Ru

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The paper investigates and characterizes linear operators preserving weak majorization of $(0, 1)$-vectors and linear operators converting vector majorization of $(0, 1)$-vectors to weak majorization.
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     title = {Linear operators preserving and converting majorizations of $(0, 1)$-vectors},
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P. M. Shteyner. Linear operators preserving and converting majorizations of $(0, 1)$-vectors. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXXV, Tome 514 (2022), pp. 204-220. http://geodesic.mathdoc.fr/item/ZNSL_2022_514_a11/

[1] A. Guterman, P. M. Shteiner, “Lineinye otobrazheniya, sokhranyayuschie mazhorizatsiyu naborov matrits”, Vestnik SPbGU, matem., 7(65) (2020), 217–229

[2] P. M. Shteiner, “Konvertatsiya stolbtsovoi mazhorizatsii”, Zap. nauchn. semin. POMI, 496, 2020, 195–215

[3] P. M. Shteiner, “Lineinye otobrazheniya, sokhranyayuschie nekotorye kombinatornye matrichnye mnozhestva”, Zap. nauchn. semin. POMI, 504, 2021, 181–199

[4] T. Ando, “Majorization, doubly stochastic matrices, and comparison of eigenvalues”, Linear Algebra Appl., 118 (1989), 163–248 | DOI | MR

[5] L. B. Beasley, S.-G. Lee, Y.-H. Lee, “A characterization of strong preservers of matrix majorization”, Linear Algebra Appl., 367 (2003), 341–346 | DOI | MR

[6] L. B. Beasley, S.-G. Lee, “Linear operators preserving multivariate majorization”, Linear Algebra Appl., 304:1 (2000), 141–159 | DOI | MR

[7] G. Dahl, “Matrix majorization”, Linear Algebra Appl., 288 (1999), 53–73 | DOI | MR

[8] G. Dahl, A. Guterman, P. Shteyner, “Majorization for matrix classes”, Linear Algebra Appl., 555 (2018), 201–221 | DOI | MR

[9] G. Dahl, A. Guterman, P. Shteyner, “Majorization for $(0,1)$-matrices”, Linear Algebra Appl., 585 (2020), 147–163 | DOI | MR

[10] J. Dieudonné, “Sur une généralisation du groupe orthogonal à quatre variables”, Arch. Math., 1 (1949), 282–287 | DOI | MR

[11] G. Frobenius, “Uber die darstellung der endlichen gruppen durch linear substitutionen”, Sitzungsber Deutsch. Akad. Wiss. Berlin, 1897, 994–1015

[12] A. Guterman, P. Shteyner, “Linear converters of weak, directional and strong majorizations”, Linear Algebra Appl., 613 (2021), 340–346 | DOI | MR

[13] A. Guterman, P. Shteyner, “Linear operators preserving strong majorization of $(0,1)$-matrices”, Linear Algebra Appl. (to appear) | MR

[14] A. M. Hasani, M. Radjabalipour, “Linear preserver of matrix majorization”, Int. J. Pure Appl. Math., 32:4 (2006), 475–482 | MR

[15] C.-K. Li, S. Pierce, “Linear preserver problems”, Amer. Math. Monthly, 108:7 (2001), 591–605 | DOI | MR

[16] C.-K. Li, E. Poon, “Linear operators preserving directional majorization”, Linear Algebra Appl., 325:1 (2001), 141–146 | MR

[17] A. W. Marshall, I. Olkin, B. C. Arnold, Inequalities: Theory of Majorization and Its Applications, second edition, Springer, New York, 2011 | MR

[18] F. D. Martinez Peria, P. G. Massey, L. E. Silvestre, “Weak matrix majorization”, Linear Algebra Appl., 403 (2005), 343–368 | DOI | MR

[19] S. Pierce et al, “A survey of linear preserver problems”, Linear Multilinear Algebra, 33:1-2 (1992), 1–119 | DOI | MR

[20] I. Schur, Einige Bemerkungen zur Determinantentheorie, Akad. Wiss., Berlin, 1925, 454–463