16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 12
Inner Product Spaces
Mathematics — Linear Algebra · self-adjoint-unitary-operators
Problem
Let V be a finite-dimensional inner product space. In Exercise 6, we showed how to construct some linear operators on V which are both self-adjoint and unitary. Now prove that there are no others, i.e., that every self-adjoint unitary operator arises from some subspace W as we described in Exercise 6.