Given the following information:
- $\Sigma \in\mathbb{R}^{n \times n}$ is symmetric positive definite and $K \in\mathbb{R}^{n \times n}$ is symmetric positive semi-definite.
- K is a kernel, $K = XX^{T}$ with $X \in\mathbb{R}^{n \times m}$, and $ m \ge n$
- Define $V = \Sigma^{-1}(I-P)$, where $ P=Z(Z^{T}\Sigma^{-1}Z)^{-1}Z^{T}\Sigma^{-1}$ is a projection matrix
- $Z \in\mathbb{R}^{n \times j}$, $j \ge 1$ and $Z$ is of full rank.
I'm interested in the properties of $A = VK$, for example is $A$ symmetric PSD?