Self-adjoint operators are used in functional analysis and quantum mechanics.

In combination with Stone's theorem on one-parameter unitary groups it shows that self-adjoint operators are precisely the infinitesimal generators of strongly continuous one-parameter unitary groups, see Self-adjoint operator # Self adjoint extensions in quantum mechanics.

A bounded linear functional on a C *- algebra A is said to be self-adjoint if it is real-valued on the self-adjoint elements of A. Self-adjoint functionals are noncommutative analogues of signed measures.

# REDIRECT Self-adjoint operator

* Self-adjoint operator

* Self-adjoint operator

where we use the symbol k to denote the quantum numbers p and σ of the previous section and the sign of the energy, E ( k ), and a < sub > k </ sub > denotes the corresponding annihilation operators.

Another special case is the class of problems where each clause only contains exclusive or operators.

It was designed to be used by untrained operators ( who would determine which keys to press by looking at the grid ), and was not used where trained telegraph operators were available.

The Lab is best known for their work on what would today be known as " interactivity ", and their machines were among the first where operators had direct control over programs running in real-time.

The earliest of these were for in-band signaling between switching centers, where long-distance telephone operators used a 16-digit keypad to input the next portion of the destination telephone number in order to contact the next downstream long-distance telephone operator.

In particular, starting in 2006 a number of operators such as Fantazzle, 365FantasySports, DraftZone, Fanduel and Snapdraft have offered daily draft games where players can draft, play and win ( or lose ) within a single day.

where is the interaction Lagrangian and signifies the time-ordered product of operators.

where signifies the normal-product of the operators and takes care of the possible sign change when commuting the fermionic operators to bring them together for a contraction ( a propagator ).

Scoreboard operators sometimes played an animated sequence of piranhas munching under that caption in situations where the Twins were scoring runs playing " small ball ", and the stadium vendors sold tee-shirts and hats advertising " The Little Piranhas ".

By transferring upper triangularisation of operators of finite-dimensional complex vector space, there is an internal orthonormal Hilbert space basis for where runs from to, such that each of the corresponding-dimensional subspaces is-invariant.

In object-oriented programming, operator overloading — less commonly known as operator ad-hoc polymorphism — is a specific case of polymorphism, where different operators have different implementations depending on their arguments.

Multiphase pumping also helps eliminate emissions of greenhouse gases as operators strive to minimize the flaring of gas and the venting of tanks where possible.

Prefix notation has seen wide application in Lisp s-expressions, where the brackets are required due to the arithmetic operators having variable arity.

In its most general formulation, quantum mechanics is a theory of abstract operators ( observables ) acting on an abstract state space ( Hilbert space ), where the observables represent physically observable quantities and the state space represents the possible states of the system under study.

Commanders and system operators need to query these databases as conveniently as possible, in an eyes-busy environment where much of the information is presented in a display format.

GEGL is modelled after a directed acyclic graph, where each node represents an image operation ( called " operators " or " ops "), and each edge represents an image.

A common alternative notation is and for positive semidefinite and positive definite matrices, respectively .</ ref > The notion comes from functional analysis where positive-semidefinite matrices define positive operators.

This ability to enable tactical communication in conditions where dedicated trained operators and hardware are inappropriate is often considered to be the true improvement offered by ALE.

In U. S. common carrier telephony service, a toll center designated Class 4C is an office where assistance in completing incoming calls is provided in addition to other traffic ; a toll center designated Class 4P is an office where operators handle only outbound calls, or where switching is performed without operator assistance.

In November 1931, Dreiser led the National Committee for the Defense of Political Prisoners ( NCDPP ) to the coalfields of southeastern Kentucky, where they took testimony from coal miners in Pineville and Harlan on the pattern of violence against the miners and their unions by the coal operators known as the Harlan County War.

The three structures are made of the primitive conditional GOTO ( IF test = true THEN GOTO step xxx ) ( a diamond ), the unconditional GOTO ( rectangle ), various assignment operators ( rectangle ), and HALT ( rectangle ).

alt = Black-and-white picture of heavy machinery with two operators sitting aside

Whereas arithmetic deals with specific numbers and operators ( e. g. 3 + 2 = 5 ), algebra introduces variables, which are letters that represent non-specified numbers ( e. g. 3a + 2a = 5a ).

The cI dimer may bind to any of three operators, OR1, OR2, and OR3, in the order OR1 = OR2 > OR3.

A chain complex is a sequence of abelian groups or modules ... A < sub > 2 </ sub >, A < sub > 1 </ sub >, A < sub > 0 </ sub >, A < sub >- 1 </ sub >, A < sub >- 2 </ sub >, ... connected by homomorphisms ( called boundary operators ) d < sub > n </ sub >: A < sub > n </ sub >→ A < sub > n − 1 </ sub >, such that the composition of any two consecutive maps is zero: d < sub > n </ sub > ∘ d < sub > n + 1 </ sub > = 0 for all n. They are usually written out as:

| crew = 4 ( 2 pilots, 2 ASW systems operators )

Many countries have now liberalized the electricity market where these risks, and the risk of cheaper competitors emerging before capital costs are recovered, are borne by plant suppliers and operators rather than consumers, which leads to a significantly different evaluation of the economics of new nuclear power plants .< ref name = MIT-2003 >

When the dimension of H is infinite, then S < sub > 1 </ sub >( H ) ( the trace class ) is not reflexive, because it contains a subspace isomorphic to ℓ < sup > 1 </ sup >, and S < sub >∞</ sub >( H ) = L ( H ) ( the bounded operators ) is not reflexive, because it contains a subspace isomorphic to ℓ < sup >∞</ sup > ( in both cases, the subspace can be chosen to be the operators diagonal with respect to a given orthonormal basis of H ).

In many applications, this condition is not strong enough, and instead a uniform ellipticity condition may be imposed for operators of degree m = 2k:

128 can be expressed by a combination of its digits with mathematical operators thus 128 = 2 < sup > 8-1 </ sup >, making it a Friedman number in base 10.

In the following, X, Y, Z, W are Banach spaces, B ( X, Y ) is the space of bounded operators from X to Y with the operator norm, K ( X, Y ) is the space of compact operators from X to Y, B ( X ) = B ( X, X ), K ( X ) = K ( X, X ), is the identity operator on X.

Corollary If M and N are normal operators, and MN =

Let Q and P be two self-adjoint operators satisfying the canonical commutation relation, = i, and s and t two real parameters.

A language may contain a fixed number of built-in operators ( e. g. +-* = in C and C ++), or it may allow the creation of programmer-defined operators ( e. g. Haskell ).

For example, the canonical operators of position and momentum have the commutator = i. ( Here, we use " natural units " where Planck's constant is set equal to 1.

V is taken to be the space of all operators at z = 0.

The extension consists of the introduction of a group G of agents, and of n modal operators K < sub > i </ sub > ( with i = 1, ..., n ) with the intended meaning that " agent i knows.

* there exist self-adjoint operators A, B such that T = A + iB, T < sup >∗</ sup > = A – iB, and for every x in the domain of T.