Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran.
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 $M_{nm}$.
Khalooei, F. (2015). Linear maps preserving or strongly preserving majorization on matrices. Bulletin of the Iranian Mathematical Society, 41(Issue 7 (Special Issue)), 77-83.
MLA
Khalooei, F. "Linear maps preserving or strongly preserving majorization on matrices", Bulletin of the Iranian Mathematical Society, 41, Issue 7 (Special Issue), 2015, 77-83.
HARVARD
Khalooei F. (2015). 'Linear maps preserving or strongly preserving majorization on matrices', Bulletin of the Iranian Mathematical Society, 41(Issue 7 (Special Issue)), pp. 77-83.
CHICAGO
F. Khalooei, "Linear maps preserving or strongly preserving majorization on matrices," Bulletin of the Iranian Mathematical Society, 41 Issue 7 (Special Issue) (2015): 77-83,
VANCOUVER
Khalooei F. Linear maps preserving or strongly preserving majorization on matrices. BIMS. 2015;41(Issue 7 (Special Issue)):77-83.
