Let be the linear transformation given by where . Demonstrate that T is unitary if and only if .
If is a unidimensional vector space, demonstrate that the only unitary linear transformations are the one given previously. In particular, if is a unidimensional vector space, there exist only 2 orthogonal transformations: and .
Attempt: Not much. I want to prove first.
If T is unitary, then . I don't know how to go further, I must show that this implies that .