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 .
and 
, then the Whitney sum 
is the vector bundle over 
such that each fiber over 
is naturally the direct sum of the 
and 
. 
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 
.