Let V be a finite dimensional vector space over the field K, V* be the dual space, the set of all linear functions on V. Now define a h:V*->K^n by h(f)=(f(e_1),f(e_2),...f(e_n)), where e_i is the basis of V. It is known that h(xf+yg)=xh(f)+yh(g), where x,y is in K and f,g in V*. It is told that h is bijective. I understand h is injective, but do not understand why it is surjective? it might be quite simple, all the books just says it is OBVIOUS, but I just don't get it.... More precisely, given x=(x_1, x_2,...,x_n) in K^n, why there is a f in V* such that h(f)=x, or equivalently, f(e_i)=x_i ? Thanks!