# antisymmetric

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Related to Anti-symmetric: Antisymmetric tensor, antisymmetric wave function, Antisymmetric matrix

## antisymmetric

(mathematics)
A relation R is antisymmetric if,

for all x and y, x R y and y R x => x == y.

I.e. no two different elements are mutually related.

Partial orders and total orders are antisymmetric. If R is also symmetric, i.e.

x R y => y R x

then

x R y => x == y

I.e. different elements are not related.
References in periodicals archive ?
It is utilized to produce anti-symmetric of last 4-bits (X (4 to 0)) when the MSB of X i.
where the anti-symmetric field tensor [PHI], given by
Finally, as a pure theory of gravitation, the results in the present work may be compared to those given in [8] and [9], wherein, based on the theory of chronometric invariants [7], a new geometric formulation of gravity (which is fully equivalent to the standard form of General Relativity) is presented in a way very similar to that of the electromagnetic field, based solely on a second-rank anti-symmetric field tensor.
ikl] are the components of the completely anti-symmetric three-dimensional Levi-Civita permutation tensor density).
Then the covariant and contravariant components of the totally anti-symmetric permutation tensor are given by
which are actually anti-symmetric with respect to the first two indices iandj.
say W, with respect to the so-called Cartan basis as the totally anti-symmetric object
kl] = 0, the components of the anti-symmetric part of the stress tensor are then given by
where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] are the covariant and contravariant components of the completely anti-symmetric Levi-Civita permutation tensor, respectively, with the ordinary permutation symbols being given as usual by [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
A spin frame is described by the anti-symmetric tensor product
x](M), we see that, astonishingly enough, the anti-symmetric product [A,B] is what defines the Lie (exterior) derivative of B with respect to A.
abcd] are the components of the completely anti-symmetric four-dimensional Levi-Civita permutation tensor and [psi] is a vector field normal to a three-dimensional space (hypersurface) [summation](t) defined as the time section ct = [x.
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