Definition of commutative in English:

commutative

adjective ˈkɒmjʊˌtətɪvkəˈmjuːtətɪv

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.
〔数〕交换的（如 a × b = b × a ）
Example sentencesExamples
- So, the addition and multiplication we are used to using are commutative.
- In the density-independent case, this multiplication is commutative.
- An operation is commutative if you can change the order of the numbers involved without changing the result.
- In the 1840s, the Irish mathematician William Hamilton found that multiplication was not commutative in all number systems.
- This is a consequence of large rotations not being commutative in three dimensions, so the averages are not accurate in regions of high variability.
2rare Relating to or involving substitution or exchange.
〈罕〉（一般）代替的；交换的
Example sentencesExamples
- 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.

Origin

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).

Definition of commutative in US English:

commutative

adjective

Mathematics

1Involving 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.
〔数〕交换的（如 a × b = b × a ）
Example sentencesExamples
- In the density-independent case, this multiplication is commutative.
- This is a consequence of large rotations not being commutative in three dimensions, so the averages are not accurate in regions of high variability.
- An operation is commutative if you can change the order of the numbers involved without changing the result.
- In the 1840s, the Irish mathematician William Hamilton found that multiplication was not commutative in all number systems.
- So, the addition and multiplication we are used to using are commutative.
1. 1.1rare Relating to or involving substitution or exchange.
  〈罕〉（一般）代替的；交换的
  Example sentencesExamples
  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.

Origin

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).

词汇	commutative
释义	Definition of commutative in English: commutative adjective ˈkɒmjʊˌtətɪvkəˈmjuːtətɪv 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. 〔数〕交换的（如 a × b = b × a ） Example sentencesExamples So, the addition and multiplication we are used to using are commutative. In the density-independent case, this multiplication is commutative. An operation is commutative if you can change the order of the numbers involved without changing the result. In the 1840s, the Irish mathematician William Hamilton found that multiplication was not commutative in all number systems. This is a consequence of large rotations not being commutative in three dimensions, so the averages are not accurate in regions of high variability. 2rare Relating to or involving substitution or exchange. 〈罕〉（一般）代替的；交换的 Example sentencesExamples 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. Origin 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). Definition of commutative in US English: commutative adjective Mathematics 1Involving 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. 〔数〕交换的（如 a × b = b × a ） Example sentencesExamples In the density-independent case, this multiplication is commutative. This is a consequence of large rotations not being commutative in three dimensions, so the averages are not accurate in regions of high variability. An operation is commutative if you can change the order of the numbers involved without changing the result. In the 1840s, the Irish mathematician William Hamilton found that multiplication was not commutative in all number systems. So, the addition and multiplication we are used to using are commutative. 1.1rare Relating to or involving substitution or exchange. 〈罕〉（一般）代替的；交换的 Example sentencesExamples 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. Origin 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).
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