positive operator proof 1. The problem statement, all variables and given/known data Prove that if T ∈ L(V) is positive, then so is Tk for every positive integer k. 2. Relevant equations 3. The attempt at a solution Let v=b1v1+...+bnvn. Now since T is positive, T has a positive square root. T=S^2. <S^2v, v>=<S^2v1, v>+...+<S^2vn, v>. Now <S^4v, v>=<S^2v1, v>^2+...+<S^2vn, v>^2 yes? Now since S^2 is positive, S^4 is positive. And since S^4 is>=S^2, <S^4v1, v>+....+<S^4vn, v> is >=<S^2v1, v>+...+<S^2vn, v> which is >=0. But this doesn't show that its true for S^2k. I remember learning about a technique called induction. Should that be used?