Volume 35 • Number 3 • 2012   • On Linear Preservers of lgw-Majorization on $\mathbf{M}_{{n,m}}$ A. Armandnejad and A. Salemi Abstract. Let $\mathbf{M}_{n,m}$ be the set of all $n\times m$ matrices with entries in $\mathbb{F}$, where $\mathbb{F}$ is the field of real or complex numbers. For $A, B\in \mathbf{M}_{n,m}$, we say that $B$ is lgw-majorized (left generalized weakly majorized) by $A$ if there exists an $n\times n$ g-row stochastic (generalized row stochastic) matrix $R$ such that $B=RA$. In this paper, we characterize all linear operators that strongly preserve lgw-majorization on $\mathbf{M}_{n,m}$ and all linear operators that strongly preserve left weak matrix majorization on $ \mathbf{M}_{n}$. 2010 Mathematics Subject Classification: Primary: 15A03, 15A04, 15A51. Full text: PDF