Unitary matrix problem

1. Mar 10, 2007

Kolahal Bhattacharya

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

I satrted this as U=adjoint of AB
u_ik=sum(j)[(a_ij)*(b_jk)]
I know then,I may take tarnspose of both sides so that we have:[(u_ki)~]=sum(j){[(b_kj)~][(a_ji)~]}
then [U~]=[B~][A~]
Then,we are done.But,this proves for real elements.I am not sure that this proves also for imaginary elements...

2. Mar 10, 2007

nrqed

The proof works exactlythe same way, you just have to include a complex conjugate of the elements when you take the adjoint. Taking the complex conjugate does not change anything to the indices, so the proof still works...you just have complex conjugates everywhere.

3. Mar 10, 2007

Kolahal Bhattacharya

OK,I thought of this possibility as I am not using any extra property of complex matrices.
Do I need to write (a_ij)* in those cases?

4. Mar 10, 2007

Dick

I think you guys are making this too complicated. By definition: