I came across the following statement
$cov(E(\mathbf{z}|y))$ is degenerate in all direction orthogonal to $Span(\mathbf{x}_1, ...,\mathbf{x}_K)$
Vector $\mathbf{z}$ is a centred random vector of size $p$, $y$ is a scalar random variable and the $\mathbf{x}_k$ are $K$ vectors of size $p$.
Does it mean that any vector orthogonal to $Span(\mathbf{x}_1, ...,\mathbf{x}_K)$ is in the kernel of the covariance matrix of $E(\mathbf{z}|y)$?
How would you interpret it?