# Commutativity

(redirected from*Noncommutative*)

Also found in: Dictionary, Wikipedia.

Related to Noncommutative: Commutative operation

The following article is from

*The Great Soviet Encyclopedia*(1979). It might be outdated or ideologically biased.## Commutativity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].

The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.