Linear Functions Preserving Sut-Majorization on RN

Linear Functions Preserving Multivariate and Directional Majorization

Let V and W be two real vector spaces and let &sim be a relation on both V and W. A linear function T : V → W is said to be a linear preserver (respectively strong linear preserver) of &sim if Tx &sim Ty whenever x &sim y (respectively Tx &sim Ty if and only if x &sim y). In this paper we characterize all linear functions T : M_{n,m} → M_{n,k} which preserve or strongly preserve multivariate an...

Linear maps preserving or strongly preserving majorization on matrices

For $A,Bin M_{nm},$ we say that $A$ is left matrix majorized (resp. left matrix submajorized) by $B$ and write $Aprec_{ell}B$ (resp. $Aprec_{ell s}B$), if $A=RB$ for some $ntimes n$ row stochastic (resp. row substochastic) matrix $R.$ Moreover, we define the relation $sim_{ell s} $ on $M_{nm}$ as follows: $Asim_{ell s} B$ if $Aprec_{ell s} Bprec_{ell s} A.$ This paper characterizes all linear p...

linear maps preserving or strongly preserving majorization on matrices

for $a,bin m_{nm},$ we say that $a$ is left matrix majorized (resp. left matrix submajorized) by $b$ and write $aprec_{ell}b$ (resp. $aprec_{ell s}b$), if $a=rb$ for some $ntimes n$ row stochastic (resp. row substochastic) matrix $r.$ moreover, we define the relation $sim_{ell s} $ on $m_{nm}$ as follows: $asim_{ell s} b$ if $aprec_{ell s} bprec_{ell s} a.$ this paper characterizes all linear p...

Linear preserving gd-majorization functions from Mn,m to Mn,k

On Linear Maps Preserving g-Majorization from Fn to Fm

Let F and Fm be the usual spaces of n-dimensional column and m-dimensional row vectors on F, respectively, where F is the field of real or complex numbers. In this paper, the relations gsmajorization, lgw-majorization, and rgw-majorization are considered on F and Fm. Then linear maps T : F → F preserving lgw-majorization or gs-majorization and linear maps S : Fn → Fm, preserving rgw-majorizatio...

linear preserving gd-majorization functions from mn,m to mn,k