An alternating bilinear form on a vector space 
over a field 
is a bilinear form 
satisfying 
for every 
. It follows that 
. When the characteristic
of 
is not 2, this condition is equivalent to being antisymmetric.
A nondegenerate bilinear form that
is alternating is a symplectic form on the vector space. If such a form exists on a finite-dimensional vector space, its dimension
is necessarily an even number.
Alternating Bilinear Form
See also
Antisymmetric, Bilinear Form, Nondegenerate Bilinear Form, Symplectic Form, Vector SpaceExplore with Wolfram|Alpha
References
Bourbaki, N. Algebra I: Chapters 1-3. Berlin, Germany: Springer-Verlag, 1989.Cite this as:
Weisstein, Eric W. "Alternating Bilinear Form." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/AlternatingBilinearForm.html