# Commutativity

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Related to Noncommutative: Commutative operation

## Commutativity

a property of the addition and multiplication of numbers expressed by the identities a + b = b + a and ab = ba. In a more general sense, the operation a * b is termed commutative if a * b = b *a. Addition and multiplication of polynomials, for example, have the property of commutativity; vector multiplication (see VECTOR PRODUCT) is not commutative since [a,b] = — [b,a].

References in periodicals archive ?
Spinelly, "Quantum-corrected finite entropy of noncommutative acoustic black holes," Annals of Physics, vol.
In free probability theory, noncommutative random variables are seen as abstract elements of some [C.sup.*]-algebra A, equipped with a trace [tau] which plays the role of the expectation in classical probability.
Rotation vector method is used to compensate for the noncommutative errors in the determination of attitude, velocity, and position.
OPFER, The Jacobi matrix for functions in noncommutative algebras, Adv.
The earlier structure of noncommutative cryptography was based on the braid based cryptography for the generalizations of the protocols.
Now, it is interesting to note that there is a class of algebras which is nonassociative and noncommutative but possesses many characteristics similar to commutative and associative algebras and has close relations with commutative algebras.
In order to characterize the new global action as a complete flow of a new vector field on a manifold, perhaps some techniques coming from noncommutative geometry might be needed.
Finally, note that the feedback solution is briefly addressed in the conference paper  and this solution is similar to that from  although the computations differ because the noncommutative polynomial rings, associated to continuous- and discrete-time systems, are different.
Free probability is understood as the noncommutative operator-algebraic version of classical probability theory (covering commutative cases).
They generalized the notion of cyclic codes by using generator polynomials in noncommutative skew polynomial rings.
Thibon, Polynomial realizations of some combinatorial Hopf algebras, Journal of Noncommutative Geometry, 8(1) (2014) 141-162.

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