antisymmetric

adjective5

1. •
   Whose sign changes on the application of a matrix transpose or some generalisation thereof.
2. •
   Whose transpose equals its negative (i.e., Mᵀ = −M);
3. •
   That changes sign when any two indices are interchanged (e.g., Tᵢⱼₖ = -Tⱼᵢₖ);
4. •
   For which B(w,v) = -B(v,w).
5. •
   Having the property that, for any two distinct elements of S, at least one is not related to the other via R; equivalently, having the property that, for any x, y ∈ S, if both xRy and yRx then x=y.

   • The standard example for an antisymmetric relation is the relation less than or equal to on the real number system. — 1987