If you've got some
vector space V and a
field F, then a
bilinear form is map M(u,v) from V×V to
F which is
linear in each argument.
That is, for all
vectors u,v,w and all
scalars a,b:
- M(u+v,w) = M(u,w)+M(v,w)
- M(u,v+w) = M(u,v)+M(u,w)
- M(av,bw) = abM(v,w)