antisymmetric

antisymmetric
adjective Date: 1923 relating to or being a relation (as “is a subset of”) that implies equality of any two quantities for which it holds in both directions <
the relation R is antisymmetric if aRb and bRa implies a = b
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New Collegiate Dictionary. 2001.

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  • Antisymmetric — In set theory, the adjective antisymmetric usually refers to an antisymmetric relation.The term antisymmetric function is sometimes used for odd function, although some meanings of antisymmetric are essentiality f ( y , x ) = − f ( x , y ). In… …   Wikipedia

  • antisymmetric — A relation is antisymmetric if whenever R xy, and R yx, then x = y …   Philosophy dictionary

  • antisymmetric — I. | ̷ ̷(ˌ) ̷ ̷ ̷ ̷| adjective Etymology: anti (I) + symmetric of a square matrix or a tensor : having the sign of every element or component changed by the interchange of any two indices of that element or component II. adjective 1. : relating… …   Useful english dictionary

  • antisymmetric — /an tee si me trik, an tuy /, adj. Math. noting a relation in which one element s dependence on a second implies that the second element is not dependent on the first, as the relation greater than. Also, antisymmetrical. [1920 25; ANTI +… …   Universalium

  • antisymmetric — adjective Of a relation R on a set S, having the property that for any two distinct elements of S, at least one is not related to the other via R. See Also: symmetric …   Wiktionary

  • antisymmetric — adjective Mathematics & Physics unaltered in magnitude but changed in sign by an arithmetical or symmetry operation …   English new terms dictionary

  • antisymmetric — an·ti·sym·met·ric …   English syllables

  • Antisymmetric tensor — In mathematics and theoretical physics, a tensor is antisymmetric on two indices i and j if it flips sign when the two indices are interchanged: An antisymmetric tensor is a tensor for which there are two indices on which it is antisymmetric. If… …   Wikipedia

  • Antisymmetric relation — In mathematics, a binary relation R on a set X is antisymmetric if, for all a and b in X , if a is R to b and b is R to a , then a = b .In mathematical notation, this is::forall a, b in X, a R b and b R a ; Rightarrow ; a = bor equally, :forall a …   Wikipedia

  • antisymmetric state — antisimetrinė būsena statusas T sritis fizika atitikmenys: angl. antisymmetric state vok. antisymmetrischer Zustand, m rus. антисимметричное состояние, n pranc. état antisymétrique, m …   Fizikos terminų žodynas

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