Antisymmetric

The word antisymmetric refers to a change to an opposite quantity when another quantity is symmetrically changed. This concept is related to that of Symmetry and Asymmetry. The difference between these three concepts can be simply illustrated with Latin letters. The character "A" is symmetric about the vertical axis while the character "B" is not. The character "S" is antisymmetric about the vertical axis since the left side is flipped relative to the right. A character such as "H" fits the definition of both symmetric and antisymmetric. In this case the correct term is symmetric.

Other uses of the term:

• Antisymmetry in linguistics.
• Antisymmetric relation in mathematics (also see below).
• Skew-symmetric matrix in matrix properties.
• Antisymmetric tensor in matricies and index subsets.

Mathematics

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 A^T = −A)
• antisymmetric tensor

See also

• Symmetry in mathematics