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In mathematics, a binary relation on a set is antisymmetric if there is no pair of distinct elements of each of which is related by to the other. More formally, is antisymmetric precisely if for all ,,, or equivalently, =.
Relationship to asymmetric and antisymmetric relations. Symmetric and antisymmetric relations. By definition, a nonempty relation cannot be both symmetric and ...
Antisymmetric or skew-symmetric may refer to: . Antisymmetry in linguistics; Antisymmetry in physics; Antisymmetric relation in mathematics; Skew-symmetric graph; Self-complementary graph
The relationship between surface word order and the possibility of wh-movement is seemingly obscure. A possible alternative to the antisymmetric explanation could be based on the difficulty of parsing languages with rightward movement.
In two dimensions, the Levi-Civita symbol is defined by: = {+ (,) = (,) (,) = (,) = The values can be arranged into a 2 × 2 antisymmetric matrix: = (). Use of the two-dimensional symbol is common in condensed matter, and in certain specialized high-energy topics like supersymmetry [1] and twistor theory, [2] where it appears in the context of 2-spinors.
Let be a skew-symmetric matrix. The determinant of satisfies = = = ().In particular, if is odd, and since the underlying field is not of characteristic 2, the determinant vanishes.
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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.