# Squared exponential kernel

The squared exponential kernel defines a stationary gaussian process and results in a *smooth prior* over the space of functions that can be sampled from the gaussian process. In 1 dimension we write:

And in \(D\) dimensions with the *covariance matrix* \(\Sigma\) between the different dimensions:

The parameter \(l\) is the characteristic lengthscale of the process. As one can see on the figure below, the larger the value of \(l\) the "further" the kernel takes non-negligible values.