Prove that if T is a unitary operator on a finite dimensional inner product space V, then T has a unitary square root. ie. there exists a unitary operator U such that T = U^2
I know that t is unitary if TT* = T*T = I, where T* is the adjoint of T
I am able to show that such a U is unitary (UUU*U* = I, therefore UU* = U*U) but i can show the existence of such a U. Anyone can help me to start the problem. Should I convert the operator to a matrix and work with matrix?