Let V be a nite-dimensional inner product space and suppose that S and T are self-adjoint. Prove that if ST 2 TS then there exists an orthonormal...

Completely lost in this question any help would mean so much, practice midterm question.

Let V be a finite-dimensional inner product space and suppose that Sand T are self-adjoint. Prove that if ST 2 TS then there exists anorthonormal basis ('01, . . . gun) of V which is an eigenbasis for both 8and T. (hint: the A-eigenspace for 8' is invariant for T and Vice versa)