if t is an isomorphism of V onto W,prove that t maps a basis of V onto a basis of W
thanks
I'll let is the isomorphism, and a basis for . Note that since is injective that (why?) and so and so is l.i. Now, since is surjective we have that for any there exists some such that . Note though that since is a basis for there exists such that and so and thus . Thus, is a basis for