I have a complex matrix and a vector of two complex numbers:
bs1 = ( {
{1/Sqrt[2], u},
{-Conjugate[u], 1/Sqrt[2]}
} )
where u is a complex number.
and the vector
state = ( {
{\[Alpha]},
{\[Beta]}
} )
where Alpha and Beta are complex numbers. The Norm of the vector should be 1
I wish to compute
Norm[bs1.state]^2
and then simplify. The result should be:
1/2 + Norm[u]^2 = 1
However this is predicated on the vector Norm being 1. How do I define the vector specifying that the norm is 1?
As an aside if the Conjugate is not defined say there was u and -u where u, Alpha and Beta are complex how would I specify that they are indeed complex variables for the symbolic evaluation?
