English

Etymology

From anti- + symmetric.

Adjective

1. 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.

Antonyms

• symmetric

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

See also Symmetry in mathematics.