Complex conjugate of a vector space
If V is a complex vector space, then any two vector spaces with a bijective antilinear map from V to it are all isomorphic. Pick a representatitive and call it the complex conjugate vector space of V. The conjugate of the conjugate of V is isomorphic to V. So, we can tweak the definition of the conjugate so that the conjugate of the conjugate of V is none other than V itself.
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