Unitary Operator


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Unitary Operator

 

an extension of the notation of a rotation of Euclidean space to the infinite-dimensional case. More precisely, a unitary operator is a rotation of a Hilbert space about the origin. In analytic terms, an operator U that maps the Hilbert space H onto itself is said to be unitary if (f, g) = (Uf,Ug) for any two vectors f, g in H. A unitary operator preserves lengths of vectors and angles between vectors and is a linear operator. A unitary operator U has a unitary inverse U–1 such that U–1 = U*, where U* is the adjoint of U.

An example of a unitary operator is the Fourier-Plancherel operator, which associates to each function f(x), – ∞ < x < ∞, with square integrable absolute value the function

References in periodicals archive ?
The unitary operator theory was developed under Berwind Natural Resources Corp.
The unitary operator test established these factors:
Then T is compact if and only if for every unitary operator [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] tends to 0 whenever [lambda] tends to the boundary points of [partial derivative][OMEGA].
If we think of the measurement as dictated by Schroedinger's equation, then we should have a unitary operator [U.
Furthermore, because any unitary operator on d qubits can be factored into a product of two-level unitary operators on d qubits (Deutsch et al.
This is based on the Hadamard transformation, a unitary operator on [l.
t] is a unitary operator defined on the tensor product H [cross product] [GAMMA]([L.
n] is a unitary operator F such that the linear functionals [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] do not define bounded linear functionals.
And because any unitary operator has a reverse operator, it implies that quantum circuits are reversible.
Let [pi] : G [right arrow] B(H) be a projective, unitary representation of the group G into the unitary operators on the Hilbert space H.
Motivated by the works of Mustari and Taylor [15,17], we have recently begun to study the mean ergodic theorem under the framework of RN modules [18] to obtain the mean ergodic theorem in the sense of convergence in probability, where we proved the mean ergodic theorem for a strongly continuous semigroup of random unitary operators defined on complete random inner product modules (briefly, complete RIP modules).
He explains vector spaces and bases, linear transformations and operators, eigenvalues, circles and ellipses, inner products, adjoints, Hermitian operators, unitary operators, the wave equation, continuous spectre and the Dirac delta function, Fourier transforms, Green's and functions, and includes an appendix on matrix operations (new to this edition) and a full chapter on crucial applications.