Majorization
In mathematics, majorization is a preorder on vectors of real numbers. For a vector 
, we denote by 
the vector with the same components, but sorted in descending order.
Given 
, we say that
weakly majorizes (or dominates) 
from below written as 
iff
where 
and 
are the elements of and , respectively, sorted in decreasing order.
Equivalently, we say that is weakly majorized (or dominated) by from below, denoted as 
.