Wiktionary
a. (context set theory English) ''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''.
Wikipedia
Antisymmetric or skew-symmetric may refer to:
- Antisymmetry in linguistics
- Antisymmetric relation in mathematics
- Skew-symmetric graph
- Self-complementary graph
In mathematics, especially linear algebra, and in theoretical physics, the adjective antisymmetric (or skew-symmetric) is used for matrices, tensors, and other objects that change sign if an appropriate operation (e.g. matrix transposition) is performed. See:
- Skew-symmetric matrix (a matrix A for which A = −A)
- Skew-symmetric bilinear form is a bilinear form B such that B(x,y)=-B(y,x) for all x and y.
- Antisymmetric tensor in matrices and index subsets.
- "antisymmetric function" – odd function
Usage examples of "antisymmetric".
The difference, however, is that a mirror rephrasing of this sort results in the antisymmetric tensor field Bμv —the real part of the complexified Kähler form on the mirror Calabi-Yau space—vanishing, and this is a far more drastic sort of singularity than that discussed in Chapter 11.