This may be a very simple question In Demailly's Complex analytic and differential geometry Chapter7,$6. Positivity concepts for vector bundles,he says:
Let $E$ be a hermitian holomorphic vector bundle of rank $r$ over $X$,where $\dim_\mathbb C=n$.Denote by $(e_1,...,e_r)$ an orthonormal frame of $E$ over a coordinate path $\Omega\subset X$ with complex coordinates $(z_1,...,z_n)$,and the Chern curvature tensor
$$i\Theta(E)=i\mkern-9mu \sum_ {\substack{1\leq j,k \leq n,\\1\leq \lambda,\mu\leq r}}{\mkern-12mu c_{j k \lambda \mu}}(x)\,\ dz_j\wedge d\overline z_k\otimes e_\lambda^*\otimes e_\mu,$$then we have $\;\overline{c_{j k \lambda \mu}}=c_{k j \mu\lambda}$.
I wonder how we can get this relationship,any references and suggestion are appreciated.Thanks a lot.