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In [[mathematics]], a '''vector-valued differential form''' on a [[manifold]] ''M'' is a [[differential form]] on ''M'' with values in a [[vector space]] ''V''. More generally, it is a differential form with values in some [[vector bundle]] ''E'' over ''M''. Ordinary differential forms can be viewed as '''R'''-valued differential forms.
An important case of vector-valued differential forms are [[Lie algebra-valued forms]]. (A [[connection form]] is an example of such a form.)
==Formal definition==
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