Let $X$ be a complex manifold, let $E \to X$ be a holomorphic vector bundle equipped with a Hermitian metric $h$, and let $\bar{\partial}_E:A^0(X;E)\to A^{0,1}(X;E)$ denote the Dolbeault operator determined by the holomorphic structure on $E$. Let $D:A^0(X;E)\to A^1(X;E)$ be the Chern connection of $(E,h)$, meaning the unique connection compatible with $h$ whose $(0,1)$ part is $D^{0,1}=\bar{\partial}_E$, and let the same symbol $D$ denote its induced exterior covariant derivative on $E$-valued forms. If $F_D := D^2 \in A^2(X;\operatorname{End}E)$ denotes the curvature of $D$, and $A^{p,q}(X;\operatorname{End}E)$ denotes the space of smooth $\operatorname{End}E$-valued forms of type $(p,q)$ on $X$, then $F_D$ has pure type $(1,1)$; equivalently, $F_D \in A^{1,1}(X;\operatorname{End}E)$.