The complex dimension of a complex vector space 
is its dimension
as a vector space over 
. A complex manifold has
complex dimension 
if its coordinate charts take values in open
subsets of 
.
The underlying real vector space of 
has twice its complex dimension, and the underlying real manifold of a complex 
-manifold has dimension 
.
Complex Dimension
See also
Complex Manifold, Complex Vector Space, Dimension, Vector SpaceExplore with Wolfram|Alpha
References
Voisin, C. Hodge Theory and Complex Algebraic Geometry I. Cambridge, England: Cambridge University Press, 2002.Cite this as:
Weisstein, Eric W. "Complex Dimension." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ComplexDimension.html