Definition, Betydelse & Synonymer | Engelska ordet COMMUTATOR

Definition av COMMUTATOR

1. (matematik) kommutator

Exempel på hur man kan använda COMMUTATOR i en mening

• In mathematics, the commutator gives an indication of the extent to which a certain binary operation fails to be commutative.
• In mathematics, more specifically in abstract algebra, the commutator subgroup or derived subgroup of a group is the subgroup generated by all the commutators of the group.
• A commutator is a rotary electrical switch in certain types of electric motors and electrical generators that periodically reverses the current direction between the rotor and the external circuit.
• In the mathematical field of representation theory, a Lie algebra representation or representation of a Lie algebra is a way of writing a Lie algebra as a set of matrices (or endomorphisms of a vector space) in such a way that the Lie bracket is given by the commutator.
• This scheme, like the earlier "card catalog," was independent of the number of connections being used in the Enigma's plugboard, or commutator.
• When contrasting the behavior of finite rotation matrices in the Baker–Campbell–Hausdorff formula above with that of infinitesimal rotation matrices, where all the commutator terms will be second-order infinitesimals, one finds a bona fide vector space.
• In mathematics, more specifically in group theory, a group is said to be perfect if it equals its own commutator subgroup, or equivalently, if the group has no non-trivial abelian quotients (equivalently, its abelianization, which is the universal abelian quotient, is trivial).
• In particular, unlike the commutator, the propagator is nonzero outside of the light cone, though it falls off rapidly for spacelike intervals.
• For example, the commutator of the creation and annihilation operators that are associated with the same boson state equals one, while all other commutators vanish.
• However, he further appreciated that such a systematic correspondence does, in fact, exist between the quantum commutator and a deformation of the Poisson bracket, today called the Moyal bracket, and, in general, quantum operators and classical observables and distributions in phase space.
• As the rotor rotates, the commutator selects different windings and the directional current is applied to a given winding such that the rotor's magnetic field remains misaligned with the stator and creates a torque in one direction.
• The commutator allows each armature coil to be energized in turn and connects the rotating coils with the external power supply through brushes.
• It led to what is now known as the "Calderón program", with major parts: Calderón's study of the Cauchy integral on Lipschitz curves, and his proof of the boundedness of the "first commutator".
• On this space, one can map all classical observables to operators on the prequantum Hilbert space, with the commutator corresponding exactly to the Poisson bracket.
• If the algebra A is noncommutative, then the commutator with respect to an element of the algebra A defines a linear endomorphism of A to itself, which is a derivation over K.
• The commutator collects all the terminations of the armature coils and distributes them in a circular pattern to allow the correct sequence of current flow.
• The subspaces should form an integrable distribution, meaning that the commutator of two vector fields lying in the subspace at each point should also lie in the subspace at each point.
• NEMA only had 5 electrical rotors vis-à-vis the Fialka's 10, and furthermore NEMA lacked a punched card commutator or equivalent such as a plug board.
• equal to its own commutator subgroup, where Diff(M, r) is the group of C^r diffeomorphisms of a smooth manifold M that are isotopic to the identity through a compactly supported C^r isotopy.
• Such representations decompose into finite-dimensional subrepresentations with respect to the subalgebras spanned by each simple root, the corresponding negative root and their commutator, which is a Cartan generator.

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