Metric independence of curvature Dolbeault powers ($\alpha (E{)}^k=[{\Theta }^k]$)

Composition of endomorphisms and wedge product of differential forms give the class $[{\Theta }^k]\in H^k(M,{\Omega }_M^k\otimes \mathrm{End}E)$. Even total degree of vector-bundle curvature and the noncommutative telescoping identity give ${\Theta }_1^k-{\Theta }_0^k=\bar{\partial }{\sum }_{j=0}^{k-1}{\Theta }_1^{j}a{\Theta }_0^{k-1-j}$ whenever ${\Theta }_1-{\Theta }_0=\bar{\partial }a$. Thus all powers are metric independent; no commutativity of endomorphisms is assumed.