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 the, 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)
“Man is more disposed to domination than freedom; and a structure of dominion not only gladdens the eye of the master who rears and protects it, but even its servants are uplifted by the thought that they are members of a whole, which rises high above the life and strength of single generations.”
—Karl Wilhelm Von Humboldt (1767–1835)
“Science is intimately integrated with the whole social structure and cultural tradition. They mutually support one other—only in certain types of society can science flourish, and conversely without a continuous and healthy development and application of science such a society cannot function properly.”
—Talcott Parsons (1902–1979)