Oops, I think I just came across a lemma that states that for a transformation to be invertible, the vector spaces have to be of the same dimension? For example, if T:V ---> W, then T is invertible if and only if dim(V) = dim(W). Is this true?
EDIT: Does this also mean that if dim(V) = dim(W) then T is invertible? Sorry, the way my book words it is differently than above and it's confusing me! Any help is appreciated!