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	Unitary operator - Wikipedia, the free encyclopedia
		Unitary matrices are precisely the unitary operators on finite-dimensional Hilbert spaces, so the notion of a unitary operator is a generalisation of the notion of a unitary matrix.
		A non-obvious example of a unitary operator is the Fourier transform (with proper normalization).
		The spectrum of a unitary operator lies on the unit circle.
	en.wikipedia.org /wiki/Unitary_operator (168 words)

	Unitary matrix - Wikipedia, the free encyclopedia
		A unitary matrix in which all entries are real is the same thing as an orthogonal matrix.
		It follows from the isometry property that all eigenvalues of a unitary matrix are complex numbers of absolute value 1 (i.e.
		All unitary matrices are normal, and the spectral theorem therefore applies to them.
	en.wikipedia.org /wiki/Unitary_matrix (208 words)

	[No title]
		The Secretary contends that the judge erred by not considering the operator status of Berwind and its three subsidiary corporations under a unitary operator theory because that theory is consistent with the language and underlying purposes of the Mine Act.
		The Secretary's unitary operator theory is based upon her construction of the definition of the statutory terms "operator" and "person" in sections 3(d) and 3(f) of the Mine Act, respectively.
		We vacate the judge's rejection of the Secretary's unitary operator theory, and hold that two or more entities may be considered a unitary operator for purposes of the Mine Act based upon consideration of their: (1) interrelation of operations, (2) common management, (3) centralized control of mine health and safety, and (4) common ownership.
	www.fmshrc.gov /decisions/commission/knt94574d.txt (16951 words)

	Unitary Operators (Site not responding. Last check: 2007-10-08)
		A linear operator whose inverse is its adjoint is called unitary.
		These operators can be thought of as generalizations of complex numbers whose absolue value is 1.
		A unitary operator preserves the ``lengths'' and ``angles'' between vectors, and it can be considered as a type of rotation operator in abstract vector space.
	vergil.chemistry.gatech.edu /notes/quantrev/node17.html (63 words)

	Secretary of Labor v. Berwind Natural Resources Corp., et. al.
		In determining operator status, however, the Commission will review and evaluate all of these forms of participation and involvement in the operation of the mine, and no particular factor will be considered controlling.
		The Secretary's unitary operator theory is based upon her construction of the definition of the statutory terms "operator" and "person" in sections 3(d) and 3(f) of the Mine Act, respectively.
		There is also some interrelationship in the operations of the four companies, due to their vertical integration with respect to the ownership and leasing of mine property.
	www.msha.gov /SOLICITOR/FMSHRC/decision/99121284.htm (16696 words)

	Quantum Operations
		External operators have no body since they are not executed within QCL, but merely serve as a hook for a binary function which implements the desired operation directly by using the numeric QC-library and is linked to the interpreter.
		The adjoint operator to a composition of unitary operators is
		As opposed to pseudo-classic operators, it is in general impossible to uncompute a unitary operator in order to free a local register again without also destroying the intended result of the computation.
	tph.tuwien.ac.at /~oemer/doc/quprog/node14.html (1622 words)

	Definition of unitary
		12:...y operator is a generalisation of the notion of a unitary matrix.
		5:...e by the [[Peter-Weyl theorem]]; in that case the unitary dual is a [[discrete space]], and the measure att...
		30: is a one-parameter unitary group of unitary operators; the infinitesimal generator of this fa...
	www.wordiq.com /dictionary/unitary.html (685 words)

	Components of a Quantum Computer
		As mentioned in 1.3.2.6, unitary operations can be described as abstract ``rotations'' in the Hilbert space.
		Operators of that kind are referred to as quantum functions.
		Unitary transformations describe the transition between machine states and thereby the temporal evolution of a quantum system.
	tph.tuwien.ac.at /~oemer/doc/quprog/node8.html (1556 words)

	Unitary operator control for ultrasonic imaging graphical user interface - US Patent 6669633 (Site not responding. Last check: 2007-10-08)
		In this manner, the operator produces the desired ultrasonic image processing results by employing both the first control and the second control from a common operating position from one hand, thereby allowing the operator to continue scanning with a free hand while continuing to control the ultrasonic imaging system.
		The other hand of the operator may therefore be employed in manipulating an ultrasonic probe attached to the ultrasonic imaging system for gathering ultrasonic data employed in the ultrasonic imaging operations.
		Since all keys employed in controlling and selecting the ultrasonic imaging operations are accessible from a common operating position, an operator may focus on the ultrasonic image of the subject and on the hand-held probe, and need not be distracted by unwieldy controls.
	www.patentstorm.us /patents/6669633.html (17732 words)

	Unitary operator -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-08)
		In (Click link for more info and facts about functional analysis) functional analysis, a unitary operator is a (Click link for more info and facts about bounded linear operator) bounded linear operator U on a (A metric space that is linear and complete and (usually) infinite-dimensional) Hilbert space satisfying
		(Click link for more info and facts about Unitary matrices) Unitary matrices are precisely the unitary operators on finite-dimensional Hilbert spaces, so the notion of a unitary operator is a generalisation of the notion of a unitary matrix.
		Unitary operators implement ((biology) similarity or identity of form or shape or structure) isomorphisms between (Click link for more info and facts about operator algebra) operator algebras.
	www.absoluteastronomy.com /encyclopedia/u/un/unitary_operator.htm (229 words)

	unitary matrix (Site not responding. Last check: 2007-10-08)
		In mathematics, a unitary matrix is a n by n complex matrix
		A matrix is unitary if and only if its columns form an orthonormal basis of C
		All eigenvalues of a unitary matrix are complex numbers of absolute value 1 (i.e.
	www.yourencyclopedia.net /unitary_matrix.html (224 words)

	Vector Spaces (Site not responding. Last check: 2007-10-08)
		Since linear operators are represented by matrices, and their action on vectors is standard matrix multiplication, it follows that applying two linear operators in succession is equivalent to matrix multiplication—and, therefore, since matrices do not in general commute, nor do linear operators.
		Transforming the operator in this way, leaving the vector space alone, is equivalent to rotating the vector space and leaving the operator alone (of course, in a system with more than one operator, the same transformation would have to be applied to all the operators).
		As previously stated, a unitary matrix is an operator that rotates an orthonormal basis into another orthonormal basis.
	landau1.phys.virginia.edu /classes/751.mf1i.fall02/751LinearAlgebra.htm (3071 words)

	Integral Transforms Covariant To Unitary Operators And Their Implications For Joint Signal Representations - Sayeed, ... (Site not responding. Last check: 2007-10-08)
		Each variable can be associated with a Hermitian operator, or equivalently and consistently, as we show, with a parameterized unitary operator.
		It is well-known that the eigenfunctions of the unitary operator define a signal representation which is invariant to the effect of the unitary operator on the signal,...
		Sayeed and D. Jones, "Integral transforms covariant to unitary operators and their implications for joint signal representations," To appear in the IEEE Trans.
	citeseer.ist.psu.edu /182067.html (852 words)

	Models of Quantum Computation
		To allow for implementation of all possible unitary transformations, a universal set of elementary gates must be available, out of which composed gates can be constructed (see 2.2.2.3).
		As opposed to the operator formalism, the gate-notation is an inherently constructive method and -- other than QTMs -- the complexity of the problem is directly reflected in the number of gates necessary to implement it.
		If this concept is to be used for the definition of unitary operators, then language elements have to be provided which account for the reversibility of unitary transformation and the non-local nature of entangled quantum bits.
	tph.tuwien.ac.at /~oemer/doc/quprog/node9.html (979 words)

	Linear Operators (Site not responding. Last check: 2007-10-08)
		The simplest linear operator is the identity operator
		If the action of a linear operator on the basis vectors is known, then the action on any vector in the vector space is determined.
		The inverse operator of A, denoted by A
	electron6.phys.utk.edu /qm1/modules/m3/operators.htm (286 words)

	APS - 2005 36th Meeting of the Division of Atomic, Molecular and Optical Physics PostDeadline - Event - Geometric Phase ... (Site not responding. Last check: 2007-10-08)
		We demonstrate how the geometric phase can be self-consistently defined in the space of unitary operators if the dynamic group of a quantum system has physically meaningful partitioning into a subgroup and complimentary coset space.
		To motivate the introduction of a geometric phase of a unitary operator, we demonstrate that this phase does not vanish even if the quantum system is in a mixed state, described by a density matrix.
		Illustrative examples of calculating the geometric phase of a unitary operator are provided for SU(2) and SU(4) groups i.e.
	meetings.aps.org /Meeting/DAMOP05/Event/30335 (156 words)

	Hilbert space setting for quantum mechanics
		The dynamical evolution of a quantum system is expressed as a unitary operator acting on the quantum state.
		A unitary operator is in effect a rotation.
		be the projection operator onto the subspace spanned by the eigenvectors, and the probability of observing
	astarte.csustan.edu /~tom/MISC/qc-article/node2.html (316 words)

	[No title] (Site not responding. Last check: 2007-10-08)
		We can also ask if it's "close to unitary": this means that it differs from a unitary by an operator X such that tr(X* X) is finite.
		I forget.) Buzzword bonus: instead of "close to unitary", people usually say a symplectic linear transformation "meets the Hilbert-Schmidt condition" if it differs from a unitary operator by an operator X for which tr(X* X) is finite.
		All such operators are compact and this was introduced as a nice sufficient condition for compactness by Hilbert and Schmidt back in the early days of functional analysis.
	www.math.niu.edu /~rusin/known-math/00_incoming/fock (418 words)

	mp_arc 00-76 (Site not responding. Last check: 2007-10-08)
		In fact Definition: Let J be period-2 unitary operator and U be linear operator.
		In the special case that the operator U^*U-I is compact this problem was solved in the positive by M.G.Krein in 1964.
		Moreover, there asserts Theorem: For every real c>0 there exists some J-unitary operator U such that (i) if L is some nonzero U-invariant subspace, then r(UL)>c; (ii) if L' is some nonzero U^{-1}-invariant subspace, then r(U^{-1}L')>c; This result applies both to the real space case and to the complex space case.
	www.ma.utexas.edu /mp_arc-bin/mpa?yn=00-76 (214 words)

	Unitary Operator Encyclopedia Article, Definition, History, Biography (Site not responding. Last check: 2007-10-08)
		Looking For unitary operator - Find unitary operator and more at Lycos Search.
		Find unitary operator - Your relevant result is a click away!
		Look for unitary operator - Find unitary operator at one of the best sites the Internet has to offer!
	www.folkartmuseum.com /encyclopedia/Unitary_operator (313 words)

	Unitary operator (Site not responding. Last check: 2007-10-08)
		Unitary matrices are precisely the unitary operators on Hilbert spaces so the notion of a operator is a generalisation of the notion a unitary matrix.
		Operator Algebras, Unitary Representations, Enveloping Algebras, and Invariant Theory/Actes Du Colloque En L'Honneur De Jacquea Dixmier: Actes Du Colloque En L'Honneur De Jacques Dixmier (Progress in)
		The term "wandering vector" is from the theory of operators in Hilbert space;-- it means that the vector in question is transformed into a family of orthogonal vectors under a prescribed set of unitary operators.
	www.freeglossary.com /Unitary (369 words)

	Good Curses; blistering reviews, blustering views etc
		The distinction between this formalism, used by some physicists and in particular Schwinger, and the requirement of the existence of a unitary or anti-unitary operator on the states implementing the substitution law, is lost in the word "transformation".
		Then a symmetry was given as a substitution law, A maps to A' for the operators A in terms of which the theory was formulated...
		Then the transformation law is inconsistent and does not exist as a transformation of the operators built out of field operators.
	www.mth.kcl.ac.uk /~streater/goodcurses.html (995 words)

	Quantum computation: theory and implementation (Site not responding. Last check: 2007-10-08)
		The subscripts indicate the qubits operated upon by a multi-bit operation: indices before the comma specify qubits to be conditioned upon (if any), and indices after the comma specify qubits to be operated upon.
		When we refer to operators in matrix form, we will order the states in lexicographic order for simplicity; this is a natural ordering since we often consider a set of qubits as a ‘register’ holding a binary representation of a number.
		For NMR quantum computation, the fundamental two-qubit computational gate is the J-coupling operator, which is the state-evolution operator corresponding to the scalar coupling of two spins for some period of time.
	www.stanford.edu /~eboyden3/mengthesis/thesis2.htm (3730 words)

	A Unitary Correlation Operator Method (ResearchIndex) (Site not responding. Last check: 2007-10-08)
		Abstract: The short range repulsion between nucleons is treated by a unitary correlation operator which shifts the nucleons away from each other whenever their uncorrelated positions are within the replusive core.
		By formulating the correlation as a transformation of the relative distance between particle pairs, general analytic expressions for the correlated wave functions and correlated operators are given.
		The decomposition of correlated operators into irreducible n--body operators is discussed.
	citeseer.ist.psu.edu /165330.html (173 words)

	No Title (Site not responding. Last check: 2007-10-08)
		It seems, however, that we have not yet succeeded in reproducing satisfactorily the relevant experimental data starting from the two-body interaction.
		A decade ago the authors proposed a new version of the unitary-model-operator approach (unitary coupled-cluster method), referred shortly to as UMOA.
		For the determination of the operator S we have adopted a new principle that S should be a solution to the decoupling equation, that is, the transformed Hamiltonian should not have any non-zero matrix element between a state in the model space and a state in its complement.
	www.phys.unsw.edu.au /~neilson/abstracts/Okamoto/Okamoto.html (239 words)

	Energy Citations Database (ECD) - Energy and Energy-Related Bibliographic Citations
		Utilization of the parameters involved in the system under consideration leads to a unitary operator formalism for dealing with eigenvalue problems.
		The existence of a unitary linear operator that transfers a known function, being predetermined for a special choice of the parameter, to the general eigenfunction is demonstrated and its properties are discussed.
		The scaling problem and virial theorem are treated in some detail by means of the unitary operator techniques.
	www.osti.gov /energycitations/product.biblio.jsp?osti_id=4116269 (155 words)

	IngentaConnect Unitary Operator and Zero-Point Fluctuation Properties of a Polar... (Site not responding. Last check: 2007-10-08)
		IngentaConnect Unitary Operator and Zero-Point Fluctuation Properties of a Polar...
		In a model polariton system, we find a unitary operator which transforms canonically from the uncoupled states to the coupled states of the phonon-photon system.
		We investigate the ground-state properties of the system and show that when the polariton system is in its lowest energy state (the vacuum state), which means that no radiation occurs, the phonon and photon subsystems can exhibit nonclassical behavior.
	www.ingentaconnect.com /content/klu/ijtp/1999/00000038/00000010/00297586 (151 words)

	Unitary Integration with Operator Splitting for Weakly Dissipative Systems - Storming Media
		Abstract: Unitary integration is a numerical method that preserves the structure of the quantum Liouville equation by evolving the density via unitary transformations.
		Unitary integrators preserve the kinematic invariants C(sub j) = trp(sup j), j = 1,..., n to all orders in the time step.
		In this way, we guarantee that all dissipation and decoherence (variation of the C(sub j)) is due to the new non-Hamiltonian terms and not to any numerical artifacts.
	www.stormingmedia.us /11/1115/A111593.html (145 words)

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