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
Famous quotes containing the words structure of and/or structure:
“Just as a new scientific discovery manifests something that was already latent in the order of nature, and at the same time is logically related to the total structure of the existing science, so the new poem manifests something that was already latent in the order of words.”
—Northrop Frye (b. 1912)
“A special feature of the structure of our book is the monstrous but perfectly organic part that eavesdropping plays in it.”
—Vladimir Nabokov (1899–1977)