commutative law

commutative law
a law asserting that the order in which certain logical operations are performed is indifferent.

* * *

Two closely related laws of number operations.

In symbols, they are stated: a + b = b + a and ab = ba. Stated in words: Quantities to be added or multiplied can be combined in any order. More generally, if two procedures give the same result when carried out in arbitrary order, they are commutative. Exceptions occur (e.g., in vector multiplication). See also associative law, distributive law.

* * *

      in mathematics, either of two laws relating to number operations of addition and multiplication, stated symbolically: a + b = b + a and ab = ba. From these laws it follows that any finite sum or product is unaltered by reordering its terms or factors. While commutativity holds for many systems, such as the real or complex numbers, there are other systems, such as the system of n × n matrices or the system of quaternions, in which commutativity of multiplication is invalid. Scalar multiplication of two vectors (to give the so-called dot product) is commutative (i.e., a·b = b·a), but vector multiplication (to give the cross product) is not (i.e., a × b = −b × a). The commutative law does not necessarily hold for multiplication of conditionally convergent series. See also associative law; distributive law.

* * *

Universalium. 2010.

Игры ⚽ Нужно сделать НИР?

Look at other dictionaries:

  • commutative law — noun : a law applicable to certain mathematical operations: the order of the elements involved is immaterial * * * Logic. a law asserting that the order in which certain logical operations are performed is indifferent. [1835 45] * * * commutative …   Useful english dictionary

  • commutative law — komutatyvumo dėsnis statusas T sritis automatika atitikmenys: angl. commutative law vok. kommutatives Gesetz, n rus. коммутативный закон, m; переместительный закон, m pranc. loi de commutativité, f ryšiai: sinonimas – perstatomumo dėsnis …   Automatikos terminų žodynas

  • commutative law — law asserting that the order in which certain operations is performed is indifferent (Mathematics) …   English contemporary dictionary

  • commutative law — /kəˈmjutətɪv lɔ/ (say kuh myoohtuhtiv law), /ˈkɒmjəteɪtɪv/ (say komyuhtaytiv) noun Logic, Mathematics a law asserting that the order in which certain logical operations are performed is indifferent; in mathematics the two commutative laws are… …  

  • commutative contract — see contract Merriam Webster’s Dictionary of Law. Merriam Webster. 1996 …   Law dictionary

  • commutative justice — >> justice. Webster s New World Law Dictionary. Susan Ellis Wild. 2000 …   Law dictionary

  • commutative — index convertible, mutual (reciprocal) Burton s Legal Thesaurus. William C. Burton. 2006 …   Law dictionary

  • Law — /law/, n. 1. Andrew Bonar /bon euhr/, 1858 1923, English statesman, born in Canada: prime minister 1922 23. 2. John, 1671 1729, Scottish financier. 3. William, 1686 1761, English clergyman and devotional writer. * * * I Discipline and profession… …   Universalium

  • Commutative property — For other uses, see Commute (disambiguation). In mathematics an operation is commutative if changing the order of the operands does not change the end result. It is a fundamental property of many binary operations, and many mathematical proofs… …   Wikipedia

  • law — law1 lawlike, adj. /law/, n. 1. the principles and regulations established in a community by some authority and applicable to its people, whether in the form of legislation or of custom and policies recognized and enforced by judicial decision. 2 …   Universalium

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”