Endomorphism bundle
= Endomorphism bundle
{title2=$\operatorname{End}E=E\otimes E^*$}
The <vector bundle> whose fibre at $p$ consists of linear maps $E_p\to E_p$. If a <local frame> changes by $e'=eg$, the coefficient matrix of an <endomorphism> changes by $T'=g^{-1}Tg$, giving smooth fibre-linear transitions. For a <line bundle> this bundle is canonically the trivial scalar bundle, because every fibre endomorphism is scalar multiplication. A <connection on a vector bundle> induces the <endomorphism bundle connection>.