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Definitions of antisymmetric:
  • adjective:   (set theory, order theory, of a binary relation R on a set S) 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.
  • adjective:   (of a matrix) Whose transpose equals its negative (i.e., Mᵀ = −M);
  • adjective:   (of a tensor) That changes sign when any two indices are interchanged (e.g., Tᵢⱼₖ = -Tⱼᵢₖ);
  • adjective:   (of a bilinear form) For which B(w,v) = -B(v,w).

(Definitions from Wiktionary)

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