Antisymmetric or skew-symmetric may refer to: *

Antisymmetry In linguistics, antisymmetry, is a theory of syntax described in Richard S. Kayne's 1994 book ''The Antisymmetry of Syntax''. Building upon X-bar theory, it proposes a universal, fundamental word order for phrases (Branching (linguistics), branchin ...

in linguistics *

in physics *

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\, \text ...

in mathematics *

Skew-symmetric graph In graph theory, a branch of mathematics, a skew-symmetric graph is a directed graph that is graph isomorphism, isomorphic to its own transpose graph, the graph formed by reversing all of its edges, under an isomorphism that is an involution (math ...

Self-complementary graph In the mathematical field of graph theory, a self-complementary graph is a graph which is isomorphic to its complement. The simplest non-trivial self-complementary graphs are the path graph and the cycle graph. There is no known characteri ...

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 matrix (mathemat ...

, 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 List of natural phenomena, natural phenomena. This is in contrast to experimental p ...

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

matrices Matrix (: matrices or matrixes) or MATRIX may refer to: Science and mathematics * Matrix (mathematics), a rectangular array of numbers, symbols or expressions * Matrix (logic), part of a formula in prenex normal form * Matrix (biology), the ...

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

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 or alternating 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 ...

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

odd function In mathematics, an even function is a real function such that f(-x)=f(x) for every x in its domain. Similarly, an odd function is a function such that f(-x)=-f(x) for every x in its domain. They are named for the parity of the powers of the ...

See also