An operation that takes two vector bundles over a fixed space and produces a new vector
bundle over the same space. If 
and 
are vector bundles over
, then the Whitney sum 
is the vector
bundle over 
such that each fiber over 
is naturally the direct sum
of the 
and 
fibers over
.
The Whitney sum is therefore the fiber for fiber direct sum of the two bundles 
and 
. An easy formal definition of the Whitney sum is that 
is the pull-back bundle of the diagonal map from 
to 
,
where the bundle over 
is 
.
