Definition of commutative in English:


Pronunciation /ˈkɒmjʊˌtətɪv//kəˈmjuːtətɪv/


  • 1Mathematics
    Involving the condition that a group of quantities connected by operators gives the same result whatever the order of the quantities involved, e.g. a × b = b × a.

    • ‘So, the addition and multiplication we are used to using are commutative.’
    • ‘In the 1840s, the Irish mathematician William Hamilton found that multiplication was not commutative in all number systems.’
    • ‘An operation is commutative if you can change the order of the numbers involved without changing the result.’
    • ‘This is a consequence of large rotations not being commutative in three dimensions, so the averages are not accurate in regions of high variability.’
    • ‘In the density-independent case, this multiplication is commutative.’
  • 2rare Relating to or involving substitution or exchange.

    • ‘Of course, the relationship between painting and philosophy is not entirely commutative.’
    • ‘The second difficulty was more damaging and, to a degree, commutative with the first.’


Mid 16th century (in the sense ‘relating to transactions between people’): from French commutatif, -ive or medieval Latin commutativus, from commutat- ‘exchanged’, from the verb commutare (see commute).