Commutative definition

kŏmyə-tātĭv, kə-myo͝otə-tĭv
Independent of order. Used of a logical or mathematical operation that combines objects or sets of objects two at a time. If a × b = b × a , the operation indicated by × is commutative.
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Relating to, involving, or characterized by substitution, interchange, or exchange.
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Of commutation; involving exchange or replacement.
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(mathematics, of a binary operation) Such that the order in which the operands are taken does not affect their image under the operation.

Addition on the real numbers is commutative because for any real numbers , it is true that .

adjective
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(algebra, of an algebraic structure) Having a commutative operation.
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(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.
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(math.) Of or pertaining to an operation in which the order of the elements does not affect the result, as, in addition, 3 + 2 = 2 + 3 and, in multiplication, 2 × 3 = 3 × 2
adjective
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Of or relating to binary operations for which changing the order of the inputs does not change the result of the operation. For example, addition is commutative, since a + b = b + a for any two numbers a and b , while subtraction is not commutative, since a − b ¬eq; a − b unless both a and b are zero.
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Origin of commutative

  • commuter +‎ -ative ("tending to substitute or switch"), from from French commuter (“to substitute or switch”) and the suffix -ative (“tending to”)

    From Wiktionary

Commutative Sentence Examples

  • Division.-From the commutative law for multiplication, which shows that 3 X 4d.

  • The effect of these definitions is that the sum and the product of two quaternions are also quaternions; that addition is associative and commutative; and that multiplication is associative and distributive, but not commutative.

  • With this notation the values of x and y may be expressed in the forms x q q /N q ', gg /Nq', which are free from ambiguity, since scalars are commutative with quaternions.

  • This idea finds fuller expression in the algebra of matrices, as to which it must suffice to say that a matrix is a symbol consisting of a rectangular array of scalars, and that matrices may be combined by a rule of addition which obeys the usual laws, and a rule of multiplication which is distributive and associative, but not, in general, commutative.

  • Multiplication may or may not be commutative, and in the same way it may or may not be associative.

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Words near commutative in the Dictionary