# commutative

[kuh-myoo-tuh-tiv, kom-yuh-tey-tiv]

- of or relating to commutation, exchange, substitution, or interchange.
- Mathematics.
- (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.
- having reference to this property: commutative law for multiplication.

Show More

## Origin of commutative

Dictionary.com Unabridged
Based on the Random House Unabridged Dictionary, © Random House, Inc. 2018

## commutative

- relating to or involving substitution
- maths logic
- (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
- relating to this propertythe commutative law of addition

Show More

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

## commutative

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

Show More

Online Etymology Dictionary, © 2010 Douglas Harper

## commutative

[kə-myōō′tə-tĭv, kŏm′yə-tā′tĭv]

- 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. See also associative distributive.

Show More

The American Heritage® Science Dictionary
Copyright © 2011. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.