Antisymmetric or skew-symmetric may refer to: *

Antisymmetry In linguistics, antisymmetry is a syntactic theory presented in Richard S. Kayne's 1994 monograph ''The Antisymmetry of Syntax''. It asserts that grammatical hierarchies in natural language follow a universal order, namely specifier-head-complem ...

in linguistics *

Antisymmetric relation In mathematics, a binary relation R on a set X is antisymmetric if there is no pair of ''distinct'' elements of X each of which is related by R to the other. More formally, R is antisymmetric precisely if for all a, b \in X, \text \,aRb\, \te ...

in mathematics *

Skew-symmetric graph In graph theory, a branch of mathematics, a skew-symmetric graph is a directed graph that is isomorphic to its own transpose graph, the graph formed by reversing all of its edges, under an isomorphism that is an involution without any fixed poi ...

* Self-complementary graph In mathematics, especially

linear algebra Linear algebra is the branch of mathematics concerning linear equations such as: :a_1x_1+\cdots +a_nx_n=b, linear maps such as: :(x_1, \ldots, x_n) \mapsto a_1x_1+\cdots +a_nx_n, and their representations in vector spaces and through matric ...

, and in

theoretical physics Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict natural phenomena. This is in contrast to experimental physics, which uses experi ...

, the adjective antisymmetric (or skew-symmetric) is used for matrices,

tensor In mathematics, a tensor is an algebraic object that describes a multilinear relationship between sets of algebraic objects related to a vector space. Tensors may map between different objects such as vectors, scalars, and even other tens ...

s, and other objects that change sign if an appropriate operation (e.g. matrix transposition) is performed. See: *

Skew-symmetric matrix In mathematics, particularly in linear algebra, a skew-symmetric (or antisymmetric or antimetric) matrix is a square matrix whose transpose equals its negative. That is, it satisfies the condition In terms of the entries of the matrix, if a ...

(a matrix ''A'' for which ) * Skew-symmetric bilinear form is a bilinear form ''B'' such that for all ''x'' and ''y''. *

Antisymmetric tensor In mathematics and theoretical physics, a tensor is antisymmetric on (or with respect to) an index subset if it alternates sign (+/−) when any two indices of the subset are interchanged. section §7. The index subset must generally either be all ...

in matrices and index subsets. * "antisymmetric function" – odd function

See also