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 .