# User Contributed Dictionary

### Adjective

#### Antonyms

# Extensive Definition

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.

antisymmetric in Japanese:
反対称性