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Abstract
Let X and Y be two matrices in . One says that X is multivariate majorized by Y, in notation
(or
), if there exists a doubly stochastic matrix D in
such that
. A linear mapping
from
into
is said to be of preserving multivariate majorization if
whenever
; a linear mapping
from
into
is said to be a local preserving multivariate majorization if, for each
, there exists a linear mapping
of preserving multivariate majorization, which is depended on X, such that
. In this paper ,we will show that a linear mapping
from
into
is of local preserving multivariate majorization if and only if
for some
in
, some R in
and some permutation matrix P in
, where
is the jth column vectors of X.
Notes
No potential conflict of interest was reported by the authors.