Complex Conjugate of A Hilbert Space
Given a Hilbert space (either finite or infinite dimensional), its complex conjugate is the same vector space as its continuous dual space . There is one-to-one antilinear correspondence between continuous linear functionals and vectors. In other words, any continuous linear functional on is an inner multiplication to some fixed vector, and vice versa.
Thus, the complex conjugate to a vector, particularly in finite dimension case, may be denoted as (v-star, a row vector which is the conjugate transpose to a column vector ). In quantum mechanics, the conjugate to a ket vector is denoted as – a bra vector (see bra-ket notation).
Read more about this topic: Complex Conjugate Vector Space
Famous quotes containing the words complex and/or space:
“It’s a complex fate, being an American, and one of the responsibilities it entails is fighting against a superstitious valuation of Europe.”
—Henry James (1843–1916)
“The merit of those who fill a space in the world’s history, who are borne forward, as it were, by the weight of thousands whom they lead, shed a perfume less sweet than do the sacrifices of private virtue.”
—Ralph Waldo Emerson (1803–1882)