On this page you'll find 10+ example sentences with Commutator. Discover the meaning, synonyms such as switch and how to use the word correctly in a sentence.
Commutator meaning
- An electrical switch, in a generator or motor, that periodically reverses the direction of an electric current.
- A binary map in a given group G, given by [g, h] = ghg⁻¹h⁻¹, where g and h are elements of G, which yields the group's identity if and only if the group operation commutes for g and h.
- A binary map in a given ring R, given by [a, b] = ab − ba, where a and b are elements of R, which yields the ring's zero element if and only if the multiplication operation commutes for a and b.
Synonyms of Commutator
Using Commutator
- The main meaning on this page is: An electrical switch, in a generator or motor, that periodically reverses the direction of an electric current. | A binary map in a given group G, given by [g, h] = ghg⁻¹h⁻¹, where g and h are elements of G, which yields the group's identity if and only if the group operation commutes for g and h. | A binary map in a given ring R, given by [a, b] = ab − ba, where a and b are elements of R, which yields the ring's zero element if and only if the multiplication operation commutes for a and b.
- Useful related words include: switch, electric switch, electrical switch.
- In the example corpus, commutator often appears in combinations such as: the commutator, commutator of, be commutator.
Context around Commutator
- Average sentence length in these examples: 27.8 words
- Position in the sentence: 3 start, 10 middle, 5 end
- Sentence types: 18 statements, 0 questions, 0 exclamations
Corpus analysis for Commutator
- In this selection, "commutator" usually appears in the middle of the sentence. The average example has 27.8 words, and this corpus slice is mostly made up of statements.
- Around the word, rotating, copper, group, subgroup, core and expression stand out and add context to how "commutator" is used.
- Recognizable usage signals include a rotating commutator with six and be a commutator. That gives this page its own corpus information beyond isolated example sentences.
- By corpus frequency, "commutator" sits close to words such as abad, abolishment and abr, which helps place it inside the broader word index.
Example types with commutator
The same corpus examples are grouped by length and sentence type, making it easier to see the contexts in which the word appears:
However, the product of two or more commutators need not be a commutator. (13 words)
Notice the commutator expression is purely formal when one of the operators is unbounded. (14 words)
Segment plate acts as insulation between the copper commutator segments of direct-current universal motors and generators. (17 words)
For instance, in any group second powers behave well, : If the derived subgroup is central, then : Ring theory The commutator of two elements a and b of a ring or an associative algebra is defined by : It is zero if and only if a and b commute. (47 words)
If a Banach algebra has unit 1, then 1 cannot be a commutator ; i.e., for any x, y ∈ A. The various algebras of functions given in the examples above have very different properties from standard examples of algebras such as the reals. (43 words)
Aside from the last event, which remained a mystery despite postflight testing of the commutator, all of the problems on Apollo 7 were quickly resolved and some of them also involved equipment or procedures that would not be used on subsequent missions. (42 words)
Example sentences (18)
Commutator and cross product The commutator of two octonions x and y is given by : This is antisymmetric and imaginary.
As a result, he was able to make the distant needle move in the direction set by the commutator on the other end of the line.
Aside from the last event, which remained a mystery despite postflight testing of the commutator, all of the problems on Apollo 7 were quickly resolved and some of them also involved equipment or procedures that would not be used on subsequent missions.
A typical high-power spark gap was a rotating commutator with six to twelve contacts per wheel, nine inches (229 mm) to a foot wide, driven by about 2,000 volts DC.
Due to the anticommutativity of the commutator, the notions of a left and right ideal in a Lie algebra coincide.
Flexible plate is used in electric motor and generator armatures, field coil insulation, and magnet and commutator core insulation.
For instance, in any group second powers behave well, : If the derived subgroup is central, then : Ring theory The commutator of two elements a and b of a ring or an associative algebra is defined by : It is zero if and only if a and b commute.
However, the product of two or more commutators need not be a commutator.
If a Banach algebra has unit 1, then 1 cannot be a commutator ; i.e., for any x, y ∈ A. The various algebras of functions given in the examples above have very different properties from standard examples of algebras such as the reals.
If X is path-connected, then this homomorphism is surjective and its kernel is the commutator subgroup of π 1 (X, x 0 ), and H 1 (X) is therefore isomorphic to the abelianization of π 1 (X, x 0 ).
Informally we can think of elements of the Lie algebra as elements of the group that are " infinitesimally close" to the identity, and the Lie bracket of the Lie algebra is related to the commutator of two such infinitesimal elements.
Notice the commutator expression is purely formal when one of the operators is unbounded.
Segment plate acts as insulation between the copper commutator segments of direct-current universal motors and generators.
The above definition of the commutator is used by some group theorists, as well as throughout this article.
The direct sum of the lower central factors is given the structure of a Lie ring by defining the bracket to be the commutator of two coset representatives.
These operators do not commute, as their (group) commutator is : which is multiplication by the constant (independent of x) (the circle group of unit modulus complex numbers).
The transmission line was operated in a 'constant current' mode, with up to 5,000 volts across each machine, some machines having double commutators to reduce the voltage on each commutator.
This shows that the commutator subgroup can be viewed as a functor on the category of groups, some implications of which are explored below.
Common combinations with commutator
These word pairs occur most frequently in English texts:
- the commutator 11×
- commutator of 4×
- be commutator 2×
- commutator subgroup 2×
- commutator is 2×