Bilinear Form:-
Let U and
V be two vector spaces over the same field F. A bilinear form on W=U⊕V is a fraction f from W into F,
which assigns to each element (α,β) in W a scalar f(α,β) in such a way that
f(aα1+bα2,β)=
af(α1,β)+bf(α2,β)
&
f(α,aβ1+bβ2)=af(α,β1)+bf(α,β2)
Here f(α,β) is an element of F. It denotes the
image of (α,β) under the function f. Thus a bilinear form on W is a function
from W into F which is linear as a function of either of its arguments when the
other is fixed.
