# Math Help - unitary matrix problem

1. ## unitary matrix problem

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. Originally Posted by kolahalb

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...
Let U=AB, then:

U(i,j) = sum(k) A(i,k)B(k,j)