%0 Journal Article %T Linear maps preserving or strongly preserving majorization on matrices %J Bulletin of the Iranian Mathematical Society %I Iranian Mathematical Society (IMS) %Z 1017-060X %A Khalooei, F. %D 2015 %\ 12/01/2015 %V 41 %N Issue 7 (Special Issue) %P 77-83 %! Linear maps preserving or strongly preserving majorization on matrices %K Linear preserver %K row substochastic matrix %K matrix majorization %R %X For $A,B\in M_{nm},$ we say that $A$ is left matrix majorized (resp. left matrix submajorized) by $B$ and write $A\prec_{\ell}B$ (resp. $A\prec_{\ell s}B$), if $A=RB$ for some $n\times n$ row stochastic (resp. row substochastic) matrix $R.$ Moreover, we define the relation $\sim_{\ell s} $ on $M_{nm}$ as follows: $A\sim_{\ell s} B$ if $A\prec_{\ell s} B\prec_{\ell s} A.$ This paper characterizes all linear preservers and all linear strong preservers of $\prec_{\ell s}$ and $\sim_{\ell s}$ from $M_{nm}$ to $M_{nm}$. %U http://bims.iranjournals.ir/article_723_2527aef09e5df50b63467d24125b54c8.pdf