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The Hom-bundle Hom(E, F) is a vector bundle whose fiber at x is the space of linear maps from E x to F x (which is often denoted Hom(E x, F x) or L(E x, F x)). The Hom-bundle is so-called (and useful) because there is a bijection between vector bundle homomorphisms from E to F over X and sections of Hom(E, F) over X.