I am trying to read through this paper - http://www.malcolmdshuster.com/Pub_2002c_J_scale_scan.pdf
Equation 2(b)from the paper says
[A] $\nu_k \equiv 2(B_k - b).\epsilon_k - |\epsilon_k|^2 $
where
[B] $\epsilon_k$ is white and Gaussian. Meaning, $\epsilon_k \sim N(0,\Sigma_k)$
The authors then say,
$\nu_k \sim N(\mu_k,\sigma_k^2)$ ---- (1)
where
$\mu_k \equiv E\{\nu_k\} = -tr(\Sigma_k)$ ---- (2)
and $\sigma_k^2 \equiv E\{\nu_k^2\}-\mu_k^2 = 4(B_k-b)^T\Sigma_k(B_k-b) + 2(tr\Sigma_k^2)$ ---- (3)
How are the authors deriving (1),(2) and (3) based on [A] and [B]?
Specifically, (1) has to do something with the fact that $\epsilon_k$ is Gaussian but I've forgotten the properties, any pointer to this is helpful. and I'm drawing a blank on how the Expected Value of $\nu_k$ is the trace of covariance matrix of $\epsilon_k$.