In mathematics, the commutator gives an indication of the extent to which a certain binary operation fails to be commutative. There are different definitions...

A commutator is a rotary electrical switch in certain types of electric motors and electrical generators that periodically reverses the current direction...

algebra, the commutator subgroup or derived subgroup of a group is the subgroup generated by all the commutators of the group. The commutator subgroup is...

material like carbon press against the commutator. The brushes make sliding contact with successive commutator segments as the rotator turns, supplying...

speed and torque of the motor. It is an improvement on the mechanical commutator (brushes) used in many conventional electric motors. The construction...

dynamo is an electrical generator that creates direct current using a commutator. Dynamos employed electromagnets for self-starting by using residual magnetic...

In mathematical physics, the ternary commutator is an additional ternary operation on a triple system defined by [ a , b , c ] = a b c − a c b − b a c...

interior product defined above and it is clear whether [·,·] denotes the commutator or the Lie bracket of vector fields. Various generalizations of the Lie...

mathematics, the commutator collecting process is a method for writing an element of a group as a product of generators and their higher commutators arranged...

the commutator subspace of a two-sided ideal of bounded linear operators on a separable Hilbert space is the linear subspace spanned by commutators of...

field coils are connected in series with the rotor windings through a commutator. It is often referred to as an AC series motor. The universal motor is...

A plugboard or control panel (the term used depends on the application area) is an array of jacks or sockets (often called hubs) into which patch cords...

A mercury swivel commutator is a connector mainly used in animal experimentation to prevent the twisting of electrode wires attached to moving animals...

L_{x},\;\;\left[L_{z},L_{x}\right]=i\hbar L_{y},} where [ , ] denotes the commutator [ X , Y ] ≡ X Y − Y X . {\displaystyle [X,Y]\equiv XY-YX.} This can be...

convergent) in X {\displaystyle X} and Y {\displaystyle Y} and iterated commutators thereof. The first few terms of this series are: Z = X + Y + 1 2 [ X...

Schrödinger picture respectively, H is the Hamiltonian and [·,·] denotes the commutator of two operators (in this case H and A). Taking expectation values automatically...

bracket of vector fields, also known as the Jacobi–Lie bracket or the commutator of vector fields, is an operator that assigns to any two vector fields...

AC was converted into DC with a commutator, a set of rotating switch contacts on the armature shaft. The commutator reversed the connection of the armature...

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...

center of E and [ , ] denotes the commutator. Equivalently, a group is quasisimple if it is equal to its commutator subgroup and its inner automorphism...

point particle in one dimension, where [x , px] = x px − px x is the commutator of x and px , i is the imaginary unit, and ℏ is the reduced Planck constant...

Poisson brackets. In quantum mechanics, it is satisfied by operator commutators on a Hilbert space and equivalently in the phase space formulation of...

of alternating current. Unlike a dynamo, a magneto does not contain a commutator to produce direct current. It is categorized as a form of alternator,...

Anshel–Anshel–Goldfeld protocol, also known as a commutator key exchange, is a key-exchange protocol using nonabelian groups. It was invented by Drs. Michael...

derivation in abstract algebra. If the algebra A is noncommutative, then the commutator with respect to an element of the algebra A defines a linear endomorphism...

{\displaystyle \textstyle \prod _{i=1}^{n}h_{i}} in H/H′, where H′ is the commutator subgroup of H. The order of the factors is irrelevant since H/H′ is abelian...

corresponds exactly to the commutator product in geometric algebra and both use the same symbol × {\displaystyle \times } . The commutator product is defined...

brackets denote the commutator. In group theory, the commutator [g, h] is commonly defined as g −1 h −1 g h . In ring theory, the commutator [a, b] is defined...

history. The Society publishes a quarterly online magazine, The Titanic Commutator, and operates a museum in Indian Orchard, Massachusetts, featuring artifacts...

current. The armature windings conduct AC even on DC machines, due to the commutator action (which periodically reverses current direction) or due to electronic...