# Matrices of forms seen as sections of a vector bundle

Given a vector bundle $\pi: E \rightarrow M$ , what are the sections of $\Omega^p(\operatorname{End} E)$? are they just matrices whose entries are $p$-forms?

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Yes, basically. Or you can think of it as $\Omega^p \otimes E \otimes E^*$ if you prefer. –  Zhen Lin Sep 21 '12 at 15:16
If you write End E in $\TeX$, you'll see $End E$, with no space between. If you write \operatorname{End}E, you'll see $\operatorname{End}E$, with proper spacing and "$\operatorname{End}$" properly non-italicized. (I fixed it.) (I see that \operatorname{End}E appears above with $E$ on the next line, so you can't see the lack of space in the code. But it's there.) –  Michael Hardy Sep 21 '12 at 16:36