Diagonalize this unitary matrix to reach .
The trace of is zero and since it is unitary it has eigenvalues with absolute value one. This mean that
What is confusing me is the fact that I am supposed to make a matrix with orthonormal column vectors out of a unitary matrix (which has orthonormal column vectors)...
Any hints are greatly appreciated, thanks!
To find the eigenvectors for , do you solve this system by elimination?
I write from row 2:
Then from row 1:
Basically I can choose y to be whatever I want, but I guess I would get the "prettiest" solution if I choose .
Is this the right way to go about it?