Hadian Nadoshan, M., Afshin, H. (2017). Latin-majorization and its linear preservers. Sahand Communications in Mathematical Analysis, 05(1), 41-47. doi: 10.22130/scma.2017.22228

Mohammad Ali Hadian Nadoshan; Hamid Reza Afshin. "Latin-majorization and its linear preservers". Sahand Communications in Mathematical Analysis, 05, 1, 2017, 41-47. doi: 10.22130/scma.2017.22228

Hadian Nadoshan, M., Afshin, H. (2017). 'Latin-majorization and its linear preservers', Sahand Communications in Mathematical Analysis, 05(1), pp. 41-47. doi: 10.22130/scma.2017.22228

Hadian Nadoshan, M., Afshin, H. Latin-majorization and its linear preservers. Sahand Communications in Mathematical Analysis, 2017; 05(1): 41-47. doi: 10.22130/scma.2017.22228

^{}Department of Mathematics, Vali-e-Asr University of Rafsanjan, Zip Code: 7718897111, Rafsanjan, Iran.

Abstract

In this paper we study the concept of Latin-majorizati-\\on. Geometrically this concept is different from other kinds of majorization in some aspects. Since the set of all $x$s Latin-majorized by a fixed $y$ is not convex, but, consists of union of finitely many convex sets. Next, we hint to linear preservers of Latin-majorization on $ \mathbb{R}^{n}$ and ${M_{n,m}}$.

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

[2] A. Armandnejad and A. Salemi, The structure of linear preservers of gs-majorization, Bull. Iranian Math. Soc., 32 (2)(2006) 31-42.

[3] R. Bhatia, Matrix Analysis, Springer-Verlag, New York, 1997.

[4] G.H. Hardy, J.E. Littlewood, and G. Polya, Inequalities, Cambridge University Press, 1988.

[5] A.M. Hasani and M. Radjabalipour, The structure of linear operators strongly preserving majorizations of matrices, Electronic Journal of Linear Algebra, 15 (2006) 260-268.

[6] F. Khalooei and A. Salemi, The Structure of linear preservers of left matrix majorization on ℝ^{p}, Electronic Journal of Linear Algebra, 18 (2009) 88-97.

[7] C.K. Li and E. Poon, Linear operators preserving directional majorization, Linear Algebra Appl., 325 (2001) 141-146.

[8] A.W. Marshall, I. Olkin, and B.C. Arnold, Inequalities: Theory of Majorization and Its Applications, Second Edition, Springer, New York, 2011.

[9] M. Niezgoda, Schur - Ostrowski type theorems revisited, J. Math. Anal. Appl., 381 (2) (2011) 935-946.

[10] J. Shao and W. Wei, A formula for the number of Latin squares, Discrete Mathematics, 110 (1992) 293-296.