Meaning ofantisymmetricin English

Adjective

1. in set theory, a relation where xRy and yRx imply x=y
   The relation is antisymmetric because it only holds when x equals y.
2. a matrix equal to its negative transpose
   In linear algebra, an antisymmetric matrix is equal to the negative of its transpose.
3. a bilinear form with B(w,v) = -B(v,w)
   A bilinear form is antisymmetric if B(w,v) equals negative B(v,w) for all vectors w and v.
4. a tensor changing sign with index swap
   The antisymmetric tensor changes its sign when the indices are swapped.