In mathematics, the complexification of a real vector space V is a vector space VC over the complex number field obtained by formally extending scalar multiplication to include multiplication by complex numbers. Any basis for V over the real numbers serves as a basis for VC over the complex numbers. == Formal definition == More generally, complexi...
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http://en.wikipedia.org/wiki/Complexification
[Lie group] In mathematics, the complexification or universal complexification of a real Lie group is given by a continuous homomorphism of the group into a complex Lie group with the universal property that every continuous homomorphism of the original group into another complex Lie group extends compatibly to a complex analytic homomorphi...
Found on
http://en.wikipedia.org/wiki/Complexification_(Lie_group)
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