Row Hadamard majorization on ${𝐌}_{m,n}$

Askarizadeh, Abbas, and Armandnejad, Ali. "Row Hadamard majorization on ${\bf M}_{m,n}$." Czechoslovak Mathematical Journal 71.3 (2021): 743-754. <http://eudml.org/doc/297927>.

@article{Askarizadeh2021,
abstract = {An $m \times n$ matrix $R$ with nonnegative entries is called row stochastic if the sum of entries on every row of $R$ is 1. Let $\{\bf M\}_\{m,n\}$ be the set of all $m \times n$ real matrices. For $A,B\in \{\bf M\}_\{m,n\}$, we say that $A$ is row Hadamard majorized by $B$ (denoted by $A\prec _\{RH\}B)$ if there exists an $m \times n$ row stochastic matrix $R$ such that $A=R\circ B$, where $X \circ Y$ is the Hadamard product (entrywise product) of matrices $X,Y\in \{\bf M\}_\{m,n\}$. In this paper, we consider the concept of row Hadamard majorization as a relation on $\{\bf M\}_\{m,n\}$ and characterize the structure of all linear operators $T\colon \{\bf M\}_\{m,n\} \rightarrow \{\bf M\}_\{m,n\}$ preserving (or strongly preserving) row Hadamard majorization. Also, we find a theoretic graph connection with linear preservers (or strong linear preservers) of row Hadamard majorization, and we give some equivalent conditions for these linear operators on $\{\bf M\}_\{n\}$.},
author = {Askarizadeh, Abbas, Armandnejad, Ali},
journal = {Czechoslovak Mathematical Journal},
keywords = {linear preserver; row Hadamard majorization; row stochastic matrix},
language = {eng},
number = {3},
pages = {743-754},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Row Hadamard majorization on $\{\bf M\}_\{m,n\}$},
url = {http://eudml.org/doc/297927},
volume = {71},
year = {2021},
}

TY - JOUR
AU - Askarizadeh, Abbas
AU - Armandnejad, Ali
TI - Row Hadamard majorization on ${\bf M}_{m,n}$
JO - Czechoslovak Mathematical Journal
PY - 2021
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 71
IS - 3
SP - 743
EP - 754
AB - An $m \times n$ matrix $R$ with nonnegative entries is called row stochastic if the sum of entries on every row of $R$ is 1. Let ${\bf M}_{m,n}$ be the set of all $m \times n$ real matrices. For $A,B\in {\bf M}_{m,n}$, we say that $A$ is row Hadamard majorized by $B$ (denoted by $A\prec _{RH}B)$ if there exists an $m \times n$ row stochastic matrix $R$ such that $A=R\circ B$, where $X \circ Y$ is the Hadamard product (entrywise product) of matrices $X,Y\in {\bf M}_{m,n}$. In this paper, we consider the concept of row Hadamard majorization as a relation on ${\bf M}_{m,n}$ and characterize the structure of all linear operators $T\colon {\bf M}_{m,n} \rightarrow {\bf M}_{m,n}$ preserving (or strongly preserving) row Hadamard majorization. Also, we find a theoretic graph connection with linear preservers (or strong linear preservers) of row Hadamard majorization, and we give some equivalent conditions for these linear operators on ${\bf M}_{n}$.
LA - eng
KW - linear preserver; row Hadamard majorization; row stochastic matrix
UR - http://eudml.org/doc/297927
ER -