Use centered featurewise matrix $X$ and perform computation using covariance matrix $\Sigma$ expression when needed.
Example as $\Sigma := (I-P)X^T X(I-P)$ we have
$$x^T\Sigma x = \left\|X(I-P)x\right\|_2^2=\left\|X((I-P)x)\right\|_2^2=\left\|X(x-Px)\right\|_2^2$$
Use centered featurewise matrix$X$ and perform computation using covariance matrix $\Sigma$ expression when needed.$\Sigma := (I-P)X^T X(I-P)$ we have
Example as