I'm writing down the covariance matrix $K$ of a vector X using squared exponential covariance function, and then evaluating the determinant of the matrix $K$. Let's say i add a new point to $X$ , and re-evaluate $det(K)$. Does the value of the determinant of this new matrix has to be larger/smaller than the one computed with the smaller vector? In other words, is the determinant of the covariance matrix somehow affected by the dimension of $X$?
N.B: Squared Exponential covariance function: $$k(x_{i},x_{j}) = \sigma * exp(-(|x_{i}-x_{j}|)^2)/2 l)$$ where $\sigma$ and $l$ are the parameters of the covariance function.
