Max Trace of U(N) Matrices: A Complex Problem

[DavidK]

Assume A is a complex N \times N matrix. It is well known that \max_{V \in U(N)} |Tr(AV)| = Tr(\sqrt{AA^{\dagger}}). But what is
\max_{V \in U(N)} Re(Tr(AV))?

U(N) is the group of unitary N \times N matrices.

(I could not preview my post properly, so I apologize for any latex-misstakes )

 

[DavidK]

You may ignore this question. It was not very difficult to show that \max_{V \in U(N)} Re(Tr(AV))=Tr(\sqrt{AA^{\dagger}}) aswell.