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^{T}]

^{T}, where x

_{1}is element in space C and y is element in C

^{n-1}. Choose theta (element in space R) such that e

^{i(theta)}x

_{1}greater than or equal to 0 and define z=e

^{i(theta)}x =[z

_{1}, B

^{T}]

^{T}, where z

_{1}is element in R is non negative and B is element in C

^{n-1}. Show that the matrix V is unitary.

V= [z

_{1}B* ]

[B -I+((1)/(1+z

_{1})) BB*]

Can someone help me get off on the right foot?

I know that to show unitary, I can prove that V

^{T}V=I.

So I can do the V

^{T}V.

What I don't understand is how to impliment what z= into my V

^{T}V. Would it be better to substitute in z

_{1}in the beginning, or simplify V

^{T}V first, then plug in? Does (x*x=1) imply that it works for (B*B) as well?