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:<math>\phi = u^{-1}\pi^*\overline{\phi}</math>
where ''u'' is viewed as a linear isomorphism <math>V \overset{\simeq}\to E_{\pi(u)} = (\pi^*E)_u</math>. φ is then a tensorial form of type ρ. Conversely, given a tensorial form φ of type ρ, the same formula defines an ''E''-valued form <math>\overline{\phi}</math> on ''M''. In particular, there is a natural isomorphism of vector spaces
:<math>\Gamma(M, E) \to \{ f: P \to V | f(ug) = \rho(g)^{-1}f(u) \}</math>.
==Notes==
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