Editing Linear complex structure (section)

=== Direct sum ===
If ''V'' is any real vector space there is a canonical complex structure on the [[direct sum of vector spaces|direct sum]] ''V'' ⊕ ''V'' given by
<math display="block">J(v,w) = (-w,v).</math>
The [[block matrix]] form of ''J'' is
<math display="block">J = \begin{bmatrix}0 & -I_V \\ I_V & 0\end{bmatrix}</math>
where <math>I_V</math> is the identity map on ''V''. This corresponds to the complex structure on the tensor product <math>\Complex \otimes_{\R} V.</math>