Let x be a nx1 vector in Cn and y = U*x is another vector in Cn, where U is a unitary matrix and * represents the conjugate transpose.
The Euclidean norm of y equals 1 if and only if the Euclidean norm of x equals 1:
||y|| = 1 if and only if ||x|| = 1.
I can't prove this statement and don't know where to start!
Thanks so much!