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:
“What is the structure of government that will best guard against the precipitate counsels and factious combinations for unjust purposes, without a sacrifice of the fundamental principle of republicanism?”
—James Madison (1751–1836)
“Each structure and institution here was so primitive that you could at once refer it to its source; but our buildings commonly suggest neither their origin nor their purpose.”
—Henry David Thoreau (1817–1862)