noncommutative
|non-com-mu-ta-tive|
🇺🇸
/ˌnɑn.kəˈmjuː.tə.tɪv/
🇬🇧
/ˌnɒn.kəˈmjuː.tə.tɪv/
order matters
Etymology
'noncommutative' originates from English, specifically formed from the prefix 'non-' and the adjective 'commutative'; 'non-' meant 'not', and 'commutative' ultimately derives from Latin 'commutare', where 'com-' meant 'together' and 'mutare' meant 'to change'.
'noncommutative' changed from the adjective 'commutative' with the addition of the prefix 'non-' in modern mathematical English. 'commutative' itself developed from Latin 'commutare' into Late Latin and French forms (e.g. 'commuter'/'commutatif') and then into English 'commute' and 'commutative'.
Initially, 'commutative' had the general sense 'able to be exchanged or changed together', and 'noncommutative' originally meant simply 'not commutative'; in mathematics it evolved to the specific meaning 'order matters' for operations or elements.
Meanings by Part of Speech
Adjective 1
describing a binary operation or algebraic structure in which the order of the operands matters (i.e., a*b does not necessarily equal b*a).
Matrix multiplication is noncommutative: AB ≠ BA in general.
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Adjective 2
characterizing operators (for example in quantum mechanics) that do not commute with each other (their composition depends on order).
In quantum mechanics, position and momentum operators are noncommutative.
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Last updated: 2025/10/22 06:35