The eigenvalues of are the complex conjugates of the eigenvalues of (link).
You have
,
.
Thus, .
Unitary is UU*=I
U* is transpose conjugate
Prove that if a matrix U is unitary, then all eigenvalues of U have absolute value of 1.
so v is also a eigenvector for U* with eigenvalue of .
Not sure how to continue?
any help would be appreciated
Thanks in advance