Structure of The Conjugate
The vector spaces and have the same dimension over the complex numbers and are therefore isomorphic as complex vector spaces. However, there is no natural isomorphism from to . (The map is not an isomorphism, since it is antilinear.)
The double conjugate is naturally isomorphic to, with the isomorphism defined by
Usually the double conjugate of is simply identified with .
Read more about this topic: Complex Conjugate Vector Space
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