The exponential kernel is defined by:
$k(x,z) = e^{-\alpha\|x-z\|}$ where $\alpha>0$, $x,z\in \Bbb{R}^d$, $\|x\|$ is the 2-norm.
The kernel matrix is defined by $K_{ij} = k(x_i,x_j)$, $i,j\in[1\ldots n]$.
How to prove that $K$ is a positive (semi-positive) definite matrix?