Is exponential of a concave function concave? is this function: $$\exp\Big(-||Ax||^2\Big)$$ concave in A?? I know that exponential of a convex function is convex, but is exponential of a concave function concave??

### Did's example

Let $f(x)=e^{-x^2}$.

Then $f'(x)=-2xe^{-x^2}$, so $f''(x)=4x^2e^{-x^2}-2e^{-x^2}=(4x^2-2)e^{-x^2}$.

$e^{-x^2}$ is always positive, but $4x^2-2$ can be positive or negative.