Let f,g be bilinear forms on a finite dimensional vector space.
(a) Suppose g is non-degenerate. Show tha there exist unique linear operators T1, T2 on V such that f(a,b)=g(T1a,b)=g(a,T2b) for all a,b.
(b) Show that this result may not be true if g is degenerate.
Although I am clueless about this question, I was wondering if it has something to do with the adjoint of a linear operator. If we have a linear operator T on a hermitian space V then = and = for all v,w in V. But then how would you relate it to the other bilinear form and how would you use the fact that one of the bilinear forms is non-degenerate?