1. The problem statement, all variables and given/known data Suppose T is in L(V) and U is a subspace of V. Prove that U is invariant under T if and only if Uperp is invariant under T*. 2. Relevant equations V = U [tex]\oplus[/tex] Uperp if v [tex]\in[/tex] V, u [tex]\in[/tex] U, w [tex]\in[/tex] Uperp, then v = u + w. <Tv, w> = <v, T*w> 3. The attempt at a solution If U is invariant under T, this means that if u [tex]\in[/tex] U, Tu [tex]\in[/tex] U. Basically the same thing for Uperp. Not really sure where to go from here. Any ideas? Thanks!