1. The problem statement, all variables and given/known data Find a third column so that U is unitary. How much freedom in column 3? [ 1/√3 i/√2 ] [1/√3 0 ] = U [i/√3 1/√2 ] 2. Relevant equations UHU=I UH=U-1 3. The attempt at a solution Obviously in order for the matrix to be unitary the inner product of their columns must be equal to zero. I've constructed to equations by multiplying the hermitian of each of the first two columns times by the third column I designated, [a] [c]. These equations are a/√3+b/√3+ci/√3=0 and -ia/√2+c/√2=0. However, I have two equations and three unknowns. Is there another way to attempt the problem? Suggestions?