commutative
Americanadjective
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of or relating to commutation, exchange, substitution, or interchange.
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Mathematics.
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(of a binary operation) having the property that one term operating on a second is equal to the second operating on the first, as a × b = b × a.
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having reference to this property.
commutative law for multiplication.
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adjective
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relating to or involving substitution
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maths logic
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(of an operator) giving the same result irrespective of the order of the arguments; thus disjunction and addition are commutative but implication and subtraction are not
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relating to this property
the commutative law of addition
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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 ≠ a − b unless both a and b are zero.
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See also associative distributive
Other Word Forms
Etymology
Origin of commutative
1525–35; < Medieval Latin commūtātīvus, equivalent to Latin commūtāt ( us ) (past participle of commūtāre; see commute, -ate 1) + -īvus -ive
Vocabulary lists containing commutative
Example Sentences
Examples are provided to illustrate real-world usage of words in context. Any opinions expressed do not reflect the views of Dictionary.com.
Since changing the order of the subtraction did not give the same result, we know that subtraction is not commutative.
From Textbooks ● Apr. 22, 2020
Since changing the order of the division did not give the same result, division is not commutative.
From Textbooks ● Apr. 22, 2020
Addition of vectors is commutative such that A + B = B + A .
From Textbooks ● Aug. 12, 2015
Because matrix multiplication is not commutative, order matters.
From Textbooks ● Feb. 13, 2015
But the term commutative has no longer much meaning when applied to the respect due to the life, the liberty, or the honor of others.
From Elements of Morals With Special Application of the Moral Law to the Duties of the Individual and of Society and the State by Janet, Paul
Definitions and idiom definitions from Dictionary.com Unabridged, based on the Random House Unabridged Dictionary, © Random House, Inc. 2023
Idioms from The American Heritage® Idioms Dictionary copyright © 2002, 2001, 1995 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company.
