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## Homework Statement

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 ]

## Homework Equations

U

^{H}U=I

U

^{H}=U

^{-1}

## 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?

[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?