Czechoslovak Mathematical Journal, Vol. 69, No. 4, pp. 1111-1121, 2019

On row-sum majorization

Farzaneh Akbarzadeh, Ali Armandnejad

Received February 12, 2018.   Published online August 7, 2019.

Abstract:  Let $\mathbb{M}_{n,m}$ be the set of all $n\times m$ real or complex matrices. For $A,B\in\mathbb{M}_{n,m}$, we say that $A$ is row-sum majorized by $B$ (written as $A\prec^{\rm rs} B$) if $R(A)\prec R(B)$, where $R(A)$ is the row sum vector of $A$ and $\prec$ is the classical majorization on $\mathbb{R}^n$. 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 $\mathbb{R}^n$ and then find the linear preservers of row-sum majorization of these relations on $\mathbb{M}_{n,m}$.
Keywords:  majorization; linear preserver; doubly stochastic matrix
Classification MSC:  15A04, 15A21
DOI:  10.21136/CMJ.2019.0084-18

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Affiliations:   Farzaneh Akbarzadeh, Ali Armandnejad, Department of Mathematics, Vali-e-Asr University of Rafsanjan, P. O. Box 7713936417, Rafsanjan, Iran, e-mail:,

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