Almost complex structure induced by a complex atlas
= Almost complex structure induced by a complex atlas
In a holomorphic chart $z^j=x^j+iy^j$, define
$$
J\frac{\partial}{\partial x^j}=\frac{\partial}{\partial y^j},
\qquad
J\frac{\partial}{\partial y^j}=-\frac{\partial}{\partial x^j}.
$$
The derivative of every holomorphic transition map is complex linear and therefore commutes with this $J$, so the chartwise definitions glue to the intrinsic <almost complex structure> of the <complex manifold>.