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.

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.

In Physics, antisymmetric exchange, also known as the Dzyaloshinskii–Moriya interaction, is a contribution to the total magnetic exchange interaction between two neighboring magnetic spins, and .