Hey guys, I was wondering how you would go about proving that the image of a transformation T, im(T), is invariant? And following that, how would you prove T(W1 [tex]\bigcap[/tex] W2) is invariant if T(W1) and T(W2) are both invariant. On an unrelated note, another questions asks to show that TX = X - (P^-1 * X * P) is a linear operation, but no matter what I do, I always come up with it showing that it's in fact not a linear operation. What do you guys think? Thanks a lot for any help ^_^.