I have been looking for a way to simplify the following equation:
$$\frac{ \textbf{A} \textbf{A}^H }{\operatorname{Tr} \left( \textbf{A} \textbf{A}^H \right)^* \operatorname{Tr} \left( \textbf{A} \textbf{A}^H \right)}$$
where $\textbf{A}$ is a $M \times P$ matrix. The elements of $\textbf{A}$ are complex numbers.
As the Trace of $\textbf{A} \textbf{A}^H$ results in positive real values (>= 0) we could rewrite the previous equation as:
$$\frac{ \textbf{A} \textbf{A}^H }{ \operatorname{Tr} \left( \textbf{A} \textbf{A}^H \right)^2}$$
I'd like to know if there is a way to simplify that equation.