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:
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In mathematics, a binary relation R on a set X is antisymmetric if, for all a and b in X, if a is related to b and b is related to a, then a = b.
Strict inequality is antisymmetric; since a < b and b < a is impossible, the antisymmetry condition is vacuously true.
There are relations which are both symmetric and antisymmetric (equality), relations which are neither symmetric nor antisymmetric (divisibility on the integers), relations which are symmetric and not antisymmetric (congruence modulo n), and relations which are not symmetric but are anti-symmetric ("is less than").
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