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Encyclopedia > Anticommutative

A mathematical operator (typically a binary operator, represented by *) is anticommutative iff it is true that "x * y = −(y * x)" for all x and y on the operator's valid domain (e.g. R for subtraction, and R3 vectors for cross products).


Examples:

See also Commutativity.








  Results from FactBites:
 
Superspace - Wikipedia, the free encyclopedia (1049 words)
This means that a bracket may be defined between any two elements of this vector space, and that this bracket reduces to the commutator on two even coordinates and on one even and one odd coordinate while it is an anticommutator on two odd coordinates.
where [a,b] is the commutator of a and b and {a,b} is the anticommutator of a and b.
The fact that the covariant derivatives anticommute with the supercharges means the supersymmetry transformation of a covariant derivative of a superfield is equal to the covariant derivative of the same supersymmetry transformation of the same superfield.
s.html (433 words)
The Maxwell equations are formed from a combinations of commutators and anticommutators of the differential operator and the electric and magnetic fields E and B respectively (for isolated charges in a vacuum.
The electric field E is the vector part of the anticommutator of the conjugates of the differential operator and the 4-potential.
The homogeneous terms are formed from the sum of both orders of the commutator and anticommutator.
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