0 a device used in some types of electric motors to change the direction in which an electric current is flowing --
At present there is no theory that systematically reduces the number of commutators to minimum.
In other words, the length function merely counts commutators.
Provided that d is small, typically we can obtain the commutator matrix and its exponential explicitly.
The degree to which the flows of two vector fields fail to commute is measured by the commutator of the two vector fields.
For the nonabelian case we give a partial characterization of the group of free invariants in terms of 'characteristic' powers of triangles and commutator words.
An essential role is played by the commutator.
In general, the number of terms counted according to power is significantly smaller than similar enumeration by the number of commutators.
A special feature of this transducer is that the output is free from any noise induced from commutator friction.
