Let T,S : V → W be two linear transformations, and suppose B1 =
{v1,...,vn} andB2 = {w1,...,wm} are bases of V and W,
respectively.
(c) Show that the vector spaces L(V,W) and Matm×n(F) are
isomorphic. (Hint: the function MB1,B2 : L(V,W) → Matm×n(F) is
linear by (a) and (b). Show that it is a bijection. A linear
transformation is uniquely specified by its action on a basis.)
need clearly proof