Abstract :
Let $\textbf{M}_{n,m}$ be the set of $n$-by-$m$
matrices with entries in the field of real numbers. A matrix $R$ in $\textbf{M}_{n}=\textbf{M}_{n,n}$ is a generalized row substochastic matrix (g-row substochastic, for short) if $Re\leq e$, where $e=(1,1,\ldots,1)^t$. For $X,$ $Y \in \textbf{M}_{n,m}$, $X$ is said to be sgut-majorized by $Y$ (denoted by $ X
\prec_{sgut} Y$) if there exists an $n$-by-$n$ upper triangular g-row substochastic matrix $R$ such that $X=RY$. This paper characterizes all
linear preservers and strong linear preservers of $\prec_{sgut}$ on $\mathbb{R}^{n}$ and $\textbf{M}_{n,m}$ respectively.
