noncommutative
1
9.9
- adjective
- /nɒnˈkɒmjʊtətɪv/
- Specialized
- In a noncommutative system, rearranging the elements can lead to different results, illustrating how order influences operations.
Examples
-
In noncommutative operations, changing the order of the numbers affects the outcome, unlike in regular arithmetic.
-
Noncommutative geometry, random matrices.
-
Considerations of modified dispersion relations and noncommutative field theories underline the importance of continued experiments designed to detect Lorentz invariance.
Academic text (2004) -
An argument that I personally find motivating is that quantum theory can be viewed as a noncommutative generalization of classical probability theory, as was first pointed out by von Neumann.
Blog text (29) -
The noncommutative extension of quantum chromodynamics leads to a modulation of the nucleon spin frequency corresponding to an energy of order 0.1 GeV<sup>-2</sup>, subNC.
Academic text (2004) -
When adding numbers, the result does not change, but in noncommutative multiplication, the order matters significantly.
Antonyms
- Specialized
1
7.9
An operation where changing the order of numbers does not change the result
Surface Forms
Morphology
noncommutative = commutative (semi-transparent) = non + commutative
The negation 'non-' is straightforward, but 'commutative' is a technical mathematical adjective that may be unfamiliar to average learners.
Etymology
Noncommutative starts with non- ('not') and the commutative part comes from an old root meaning 'to change' or 'swap'. So noncommutative describes an action where swapping the order of things changes the result.