Hi,

i have two questions that seem to bother me lately. Maybe you could help me and/or point me in any related literature.

1) Assume hermitian matrix $H \in \mathcal{C}^{n \times n}$ that has rank $r$. How many real valued parameters are needed to describe it?

2) Now assume that you also have the knowledge that $H = G^*G$ for some $G \in \mathcal{C}^{n \times m}$ with rank r. Does this piece of information reduce the number of real valued parameters needed to specify H?

Thank you very much for your help,

Alex