On row-sum majorization

Akbarzadeh, Farzaneh, and Armandnejad, Ali. "On row-sum majorization." Czechoslovak Mathematical Journal 69.4 (2019): 1111-1121. <http://eudml.org/doc/294661>.

@article{Akbarzadeh2019,
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 $T\colon \mathbb \{M\}_\{n,m\}\rightarrow \mathbb \{M\}_\{n,m\}$ 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 $\mathbb \{M\}_\{n,m\}$.},
author = {Akbarzadeh, Farzaneh, Armandnejad, Ali},
journal = {Czechoslovak Mathematical Journal},
keywords = {majorization; linear preserver; doubly stochastic matrix},
language = {eng},
number = {4},
pages = {1111-1121},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On row-sum majorization},
url = {http://eudml.org/doc/294661},
volume = {69},
year = {2019},
}

TY - JOUR
AU - Akbarzadeh, Farzaneh
AU - Armandnejad, Ali
TI - On row-sum majorization
JO - Czechoslovak Mathematical Journal
PY - 2019
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 69
IS - 4
SP - 1111
EP - 1121
AB - 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 $T\colon \mathbb {M}_{n,m}\rightarrow \mathbb {M}_{n,m}$ 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 $\mathbb {M}_{n,m}$.
LA - eng
KW - majorization; linear preserver; doubly stochastic matrix
UR - http://eudml.org/doc/294661
ER -