Let's say I have the following maximization problem:
$max_U{tr(AU)}$
where $A\in\mathbb{C}$ and $UU^\dagger=1$
I know that for $A\in\mathbb{R}$ and $UU^T=1$ the solution is:
$U=XZ^T$ where $X$ and $Z$ come from the SVD of $A$, i.e. $A=XYZ^T$
Does this also hold for the complex case? Namely:
$U=XZ^\dagger$ with $A=XYZ^\dagger$
If so, do you have a reference to a proof?