Antisymmetric

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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 x^TAy = − y^TAx)
antisymmetric tensor