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:
“The verbal poetical texture of Shakespeare is the greatest the world has known, and is immensely superior to the structure of his plays as plays. With Shakespeare it is the metaphor that is the thing, not the play.”
—Vladimir Nabokov (1899–1977)
“With sixty staring me in the face, I have developed inflammation of the sentence structure and definite hardening of the paragraphs.”
—James Thurber (1894–1961)