TY - JOUR
T1 - Linear Functions Preserving Sut-Majorization on RN
TT -
JF - IJMSI
JO - IJMSI
VL - 11
IS - 2
UR - http://ijmsi.ir/article-1-549-en.html
Y1 - 2016
SP - 111
EP - 118
KW - (Strong) linear preserver
KW - Row substochastic matrix
KW - Sut-Majorization.
N2 - Suppose $textbf{M}_{n}$ is the vector space of all $n$-by-$n$ real matrices, and let $mathbb{R}^{n}$ be the set of all $n$-by-$1$ real vectors. A matrix $Rin textbf{M}_{n}$ is said to be $textit{row substochastic}$ if it has nonnegative entries and each row sum is at most $1$. For $x$, $y in mathbb{R}^{n}$, it is said that $x$ is $textit{sut-majorized}$ by $y$ (denoted by $ xprec_{sut} y$) if there exists an $n$-by-$n$ upper triangular row substochastic matrix $R$ such that $x=Ry$. In this note, we characterize the linear functions $T$ : $mathbb{R}^n$ $rightarrow$ $mathbb{R}^n$ preserving (resp. strongly preserving) $prec_{sut}$ with additional condition $Te_{1}neq 0$ (resp. no additional conditions).
M3 10.7508/ijmsi.2016.02.008
ER -