For the zero-mean complex random vector z = xc ixs, with cov(z) = = C iQ, with = , define w

For the zero-mean complex random vector z = xc − ixs, with cov(z) =

Σ = C − iQ, with Σ = Σ∗, define w = 2Re(a∗z), where a = ac − ias is an arbitrary non-zero complex vector. Prove cov(w) = 2a∗Σa.

Recall ∗ denotes the complex conjugate transpose.