### Definition of Commutative

1. Adjective. (of a binary operation) independent of order; as in e.g.. "A x b = b x a"

Category relationships: Math, Mathematics, Maths
Similar to: Independent
Derivative terms: Commutate

### Definition of Commutative

1. a. Relative to exchange; interchangeable; reciprocal.

### Definition of Commutative

1. Adjective. (mathematics of a binary operation) Such that the order in which the operands are taken does not affect their image under the operation. ¹

2. Adjective. (algebra of an algebraic structure) Having a commutative operation. ¹

3. Adjective. (mathematics of a diagram of morphisms) Such that any two sequences of morphisms with the same initial and final positions compose to the same morphism. ¹

¹ Source: wiktionary.com

### Commutative Pictures

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### Lexicographical Neighbors of Commutative

 communizescommunizingcommutabilitiescommutabilitycommutablecommutablenesscommutantcommutantscommutatecommutated commutatescommutatingcommutationcommutation ticketcommutationscommutative (current term)commutative algebracommutative groupcommutative justicecommutatively commutativenesscommutativitiescommutativitycommutatorcommutator lengthcommutator lengthscommutator subgroupcommutator subgroupscommutatorscommute

### Literary usage of Commutative

Below you will find example usage of this term as found in modern and/or classical literature:

1. Projective Geometry by Oswald Veblen, John Wesley Young (1910)
"The commutative law for multiplication. With the aid of Assumption P we will ... The operation of multiplication is commutative; ie ivc have Px - Py = Py ..."

2. Theory and Applications of Finite Groups by George Abram Miller, Hans Frederick Blichfeldt, Leonard Eugene Dickson (1916)
"the two substitutions ab - cd, ac - bd are commutative, but ab - cd is not commutative with be. Two substitutions which have no letter in common are always ..."

3. A Manual of Quaternions by Charles Jasper Joly (1905)
"[CHAP. i. in which they are added, or the addition of two vectors is a commutative operation.* ART. 3. The sum obtained by adding any vector CD f to the sum ..."

4. The Foundations of Geometry by David Hilbert (1902)
"For a non-archimedean number system, the commutative law of multiplication is not a necessary consequence of the remaining laws of operation; that is to say ..."

5. Lectures on the Moral Government of God by Nathaniel William Taylor (1859)
"Justice commonly classified as commutative, distributive, and general. ... By commutative justice they mean a disposition to fulfill contracts. ..."

6. An Elementary Treatise on the Differential Calculus Founded on the Method of by William Woolsey Johnson (1904)
"The result arrived at above may be expressed thus: the operations of taking the derivative with respect to two independent variables are commutative; ..."

7. Aquinas Ethicus: Or, The Moral Teaching of St. Thomas. A Translation of the by Thomas, Joseph Rickaby (1896)
"ARTICLE I.—7s restitution an act of commutative justice ? R. To restore is nothing else than to re-establish a man in the possession or ownership of that ..."

8. Elements of Quaternions by Arthur Sherburne Hardy (1895)
"It follows directly from the definition of multiplication, as applied to rectangular unit vectors, that the commutative property of algebraic factors does ..."