Noncommutativity

Part of speech: noun

Definitions

1. The characteristic of operations in which changing the order of operands results in a different output
2. A property in mathematics where the sequence of operations influences the final result and does not yield the same value
3. The quality of certain operations in which reversing the sequence of elements changes the result

Etymology: "Noncommutativity" is a plain compound: the prefix "non-" (from Latin "non", "not") attached to "commutativity," the noun form of "commutative." The base word traces back to Latin "commutare," meaning "to change altogether" or "to exchange," built from "com-" (together) and "mutare" (to change). In mathematics, "commutative" describes an operation where the order of the operands does not matter, as in addition or multiplication, so "noncommutativity" names the opposite property. The term is most at home in algebra, where it became essential once mathematicians began studying systems in which order does matter. Matrix multiplication is the classic example: multiplying matrix A by matrix B often gives a different result than multiplying B by A. Recognising this kind of behaviour is what allows the word to describe a whole class of operations rather than a single exception.

Synonyms: nonexchangeability, nonassociativity, incompatibility, asymmetry, irregularity

Antonyms: commutativity, exchangeability, symmetry, regularity, compatibility