I have a theorem without proof. I have searched many books and tried on myself, but i still dont have the solution.
Let M and N F-vector spaces, T be a base of M ,S be a base of N such that dimension of M is equal with dimension of N and f:MxN->F be a bilinear transformation. Then,
f is dual bilinear maps iff M(f,T,S) is regular matrix.
(where M(f,T,S) is a matrix of f dual bilinear transformation according to the bases T and S.)