Recent content by nojojo121

My mistake. You are completely right, unitary operators must preserve the inner product and not just the norm.

I think you are misunderstanding my usage of ##B##, which is just an arbitrary matrix used to define the inner product. This is essentially the linear equation I am trying to solve: $$ \operatorname{tr}(A^\dagger X^\dagger XA-A^\dagger X^\dagger AX-X^\dagger A^\dagger XA+X^\dagger A^\dagger...

I poorly worded what is being searched. I need to find all the matrices ##X## that make the operator ##L## unitary. As someone else mentioned above I think there is a loss in translation but what I call inner product you call dot product. So essentially I have to show for which ##X## the...

Thanks for the reply. I should have been more specific. My definition for the operator is like you guessed, that is ##L(A)=\mathfrak{ad}(X)(A)=[X,A]=X\cdot A-A\cdot X## and ##L\, : \,M{_{n\times n} } \longmapsto M{_{n\times n}} ##. The inner product is ##(A,B)= \operatorname{tr}(A{^\dagger} B)...

Unitary operator If an operator L(A) = [X, A], are there matrix X for which the operator is unitary? Keep in mind it is in a complex matrix space with standard inner product (A, B) = tr(A*B)