Linear Maps which Preserve or Strongly Preserve Weak Majorization

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...

Periodic Maps Which Preserve a Complex Structure

Linear operators that strongly preserve graphical properties of matrices - II

Beasley, L.B. and N.J. Pullman, Linear operators that strongly preserve graphical properties of matrices, Discrete Mathematics 104 (1992) 143-157. An operator on the set Ju of n X n matrices strongly preserves a subset 9 if it maps 9 into 9 and A\% into A\%. The operator semigroup of 9 is the semigroup of linear operators strongly preserving 9. We show that all the n x n matrix-families which a...

Linear operators that strongly preserve regularity of fuzzy matrices

An n× n fuzzy matrix A is called regular if there is an n× n fuzzy matrix G such that AGA = A. We study the problem of characterizing those linear operators T on the fuzzy matrices such that T (X) is regular if and only if X is. Consequently, we obtain that T strongly preserves regularity of fuzzy matrices if and only if there are permutation matrices P and Q such that it has the form T (X) = P...