If $f(x) \in \Re$ has the positive definite property, $\sum_i\sum_j a_i a_j f(x) \geq 0$ for $a_i,a_j \in \Re$, then $e^{f(x)}$ has the positive definite property.
How can i prove it?
And, i guess a composition function $g(f(x))$ has the positive definite property, if $g(x)$ is a monotonically increasing function. Is it right?