# Commutativity

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## 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 ?
Koc, Notes on commutativity of prime rings with generalized derivations, Commun.
Q] are identical modulo associativity and commutativity of "[conjunction]" and "[disjunction]".
This note defines a scalar measure of the commutativity of two orthogonal projections.
Intuitively, the idempotence of + is needed to get a partial order over the elements of the semiring (otherwise we would not have reflexivity); the commutativity of x allows us to consider sets of constraints (instead of ordered tuples); and the fact that 1 is the absorbing element of + makes the element 1 the maximum element of the partial order.
In the case of L(H), this is equivalent to the commutativity of the respective projection operators onto the subspaces p and q, and is associated in the physical interpretation with the notion of "simultaneous observability".
Also, commutativity was assumed; that is, the fare from Toronto to Montreal and return is the same as the airfare from Montreal to Toronto and return.
Additional Key Words and Phrases: Atomic operations, commutativity analysis, synchronization, optimistic synchronization, parallel computing, parallelizing compilers
For instance, commutativity of operations makes possible the interleaving (without blocking) of transactions on a given object.
x + y = y + x % Commutativity of + (x + y) + z = x + (y + z) % Associativity of + n(n(n(x) + y) + n (x + y)) = y % Robbins axiom From a set-theoretic perspective, + can be thought of as union and the function n as complement.
where the commutativity of the upper diagram follows from the fact that [[psi].
In the course of thus acting on the world and reflecting on his actions, he invents the principle of commutativity.

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