If we adjust each member of the base 
by D, then we obtain a new
base 
, the base of adjusted versions of the
elements of B. We call this the base adjusted by 
, written {B/D}. The belief structure with this base is termed the adjusted belief
structure of B by D and is written 
. To simplify our notation,
we also use to represent the vector 
,
where appropriate.
We may view as representing a belief structure over the
linear space 
. However, it is also useful to view
as an inner product space constructed over the linear space 
but with
the covariance inner product replaced by the adjusted covariance inner product
We now analyse the differences between the variance and the adjusted variance inner products.