@article {
author = {Khalooei, F.},
title = {Linear maps preserving or strongly preserving majorization on matrices},
journal = {Bulletin of the Iranian Mathematical Society},
volume = {41},
number = {Issue 7 (Special Issue)},
pages = {77-83},
year = {2015},
publisher = {Iranian Mathematical Society (IMS)},
issn = {1017-060X},
eissn = {1735-8515},
doi = {},
abstract = {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 $M_{nm}$.},
keywords = {Linear preserver,row substochastic matrix,matrix majorization},
url = {http://bims.iranjournals.ir/article_723.html},
eprint = {http://bims.iranjournals.ir/article_723_2527aef09e5df50b63467d24125b54c8.pdf}
}