The problem statement, all variables and given/known data Let T be a homomorphism from V into W. Using T, define a homomorphism T* of Hom(W, F) into Hom(V, F). Note on notation Hom(V, F) is just the dual space of V. Similarly for Hom(W, F). The attempt at a solution This is a problem from Hernstein's "Topics in Algebra". It is given before the sections covering linear independence, bases and dual spaces, which I find odd. I don't have much to work with here. The only T* I can define at this point is the one sending everything in Hom(W, F) to the 0 functional in Hom(V, F). Any tips?