antisymmetric
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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 operator notation the latter is called
anticommutativity
.In
linear algebra
and
theoretical physics
, the adjective antisymmetric (or skew-symmetric) is used for
matrices
,
tensors
, and other objects that change sign if an appropriate operation (usually the exchange of two indices, which becomes the
transposition
of the matrix) is performed. See:
antisymmetric matrix
(a matrix A for which xTAy = − yTAx)
antisymmetric tensor
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antisymmetric
<
mathematics
> A
relation
x == y.
I.e. no two different elements are mutually related.
Partial orders
and
total orders
are antisymmetric. If R is also
symmetric
x == y
I.e. different elements are not related.
(1995-04-18)
(c) Copyright 1993 by Denis Howe
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