Commutativity

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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 It might be outdated or ideologically biased.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.
References in periodicals archive ?
Zhang, "Testing spatial noncommutativity via rydberg atoms," Physical Review Letters, vol.
Note that in [31], we give detailed analysis of the core role of noncommutativity on resisting Shor's quantum algorithm attacks.
Due to noncommutativity, it clearly matters whether, for [absolute value of i-j] = 1, [G.sub.i] is positioned to the left or to the right of [G.sub.j].
Angelaki, "Do motoneurons encode the noncommutativity of ocular rotations?" Neuron, vol.
Since their introduction by Fueter ([6]) in 1935, they are called regular functions, and the same name is reserved to the solutions of three other type of equations which take into the account the noncommutativity of the quaternionic field H and the conjugate quaternionic variable [bar.q] = t - ix - jy - kz.
The main problem relates to the noncommutativity of matrix multiplication.
French-Japanese Symposia of Noncommutativity and Singularitites.
He followed that procedure by which the Riemann-Christoffel tensor was built: proceeding from the noncommutativity of the second derivatives of an arbitrary vector
--The noncommutativity of measurements--the temporal sequence of the measurements of two complementary variables makes a difference (e.g., in an interview the temporal order of the questions asked can influence the responses).
This emphasis on the observable, along with certain peculiarities of matrix mathematics (noncommutativity), led Heisenberg to the formulation of his uncertainty principle.
The noncommutativity of conjugate variables and the inseparability of object and measuring instrument are closely related to ideas expressed in interbehavioral psychology early in this century.
There are several other issues that lead to Lorentz violation such as loop quantum gravity [4, 5], geometrical effects such as noncommutativity [6, 7], torsion [8], and nonmetricity [9].