Abstract
Let \(\mathbb{M}_{n,m}\) be the set of all n × m real or complex matrices. For A, B ∈ \(\mathbb{M}_{n,m}\), we say that A is row-sum majorized by B (written as A ≺rsB) if R(A) ≺ R(B), where R(A) is the row sum vector of A and ≺ is the classical majorization on ℝn. In the present paper, the structure of all linear operators \(T : \mathbb{M}_{n,m} \rightarrow \mathbb{M}_{n,m}\) preserving or strongly preserving row-sum majorization is characterized. Also we consider the concepts of even and circulant majorization on ℝn and then find the linear preservers of row-sum majorization of these relations on \(\mathbb{M}_{n,m}\).
Similar content being viewed by others
References
T. Ando: Majorization, doubly stochastic matrices, and comparison of eigenvalues. Linear Algebra Appl. 118 (1989), 163–248.
A. Armandnejad, H. Heydari: Linear preserving gd-majorization functions from M n,m to M n,k. Bull. Iran. Math. Soc. 37 (2011), 215–224.
R. Bhatia: Matrix Analysis. Graduate Texts in Mathematics 169, Springer, New York, 1997.
A. M. Hasani, M. Radjabalipour: The structure of linear operators strongly preserving majorizations of matrices. Electron. J. Linear Algebra 15 (2006), 260–268.
S. M. Motlaghian, A. Armandnejad, F. J. Hall: Linear preservers of Hadamard majorization. Electron. J. Linear Algebra 31 (2016), 593–609.
M. Soleymani, A. Armandnejad: Linear preservers of circulant majorization on ℝn. Linear Algebra Appl. 440 (2014), 286–292.
M. Soleymani, A. Armandnejad: Linear preservers of even majorization on M n,m. Linear Multilinear Algebra 62 (2014), 1437–1449.
Author information
Authors and Affiliations
Corresponding authors
Rights and permissions
About this article
Cite this article
Akbarzadeh, F., Armandnejad, A. On Row-Sum Majorization. Czech Math J 69, 1111–1121 (2019). https://doi.org/10.21136/CMJ.2019.0084-18
Received:
Published:
Issue Date:
DOI: https://doi.org/10.21136/CMJ.2019.0084-18