• synonyms


[kuh-myoo-tuh-tiv, kom-yuh-tey-tiv]
  1. of or relating to commutation, exchange, substitution, or interchange.
  2. Mathematics.
    1. (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.
    2. having reference to this property: commutative law for multiplication.
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Origin of commutative

1525–35; < Medieval Latin commūtātīvus, equivalent to Latin commūtāt(us) (past participle of commūtāre; see commute, -ate1) + -īvus -ive
Related formscom·mu·ta·tive·ly, adverbcom·mu·ta·tiv·i·ty, nounnon·com·mu·ta·tive, adjectiveun·com·mu·ta·tive, adjectiveun·com·mu·ta·tive·ly, adverbun·com·mu·ta·tive·ness, noun
Dictionary.com Unabridged Based on the Random House Unabridged Dictionary, © Random House, Inc. 2018

British Dictionary definitions for noncommutative


  1. relating to or involving substitution
  2. maths logic
    1. (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
    2. relating to this propertythe commutative law of addition
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Derived Formscommutatively, adverb
Collins English Dictionary - Complete & Unabridged 2012 Digital Edition © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012

Word Origin and History for noncommutative



1530s, from Medieval Latin commutativus, from Latin commutat-, past participle stem of commutare (see commute (v.)).

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Online Etymology Dictionary, © 2010 Douglas Harper

noncommutative in Science


[kə-myōōtə-tĭv, kŏmyə-tā′tĭv]
  1. 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 - ba - b unless both a and b are zero. See also associative distributive.
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The American Heritage® Science Dictionary Copyright © 2011. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.