Complex Conjugation
The complexified vector space VC has more structure than an ordinary complex vector space. It comes with a canonical complex conjugation map:
defined by
The map χ may either be regarded as a conjugate-linear map from VC to itself or as a complex linear isomorphism from VC to its complex conjugate .
Conversely, given a complex vector space W with a complex conjugation χ, W is isomorphic as a complex vector space to the complexification VC of the real subspace
In other words, all complex vector spaces with complex conjugation are the complexification of a real vector space.
For example, when W = Cn with the standard complex conjugation
the invariant subspace V is just the real subspace Rn.
Read more about this topic: Complexification
Famous quotes containing the word complex:
“I have met charming people, lots who would be charming if they hadn’t got a complex about the British and everyone has pleasant and cheerful manners and I like most of the American voices. On the other hand I don’t believe they have any God and their hats are frightful. On balance I prefer the Arabs.”
—Freya Stark (1893–1993)