Consider a real, symmetric matrix $M(t)$ with time-varying elements. Each of the elements are zero for $t<0$ and positive for $t\geq 0$. Assume that $M(t)\succeq 0 \;\forall t\geq 0$ (i.e., it is positive semidefinite).
Is the following matrix obtained by taking Laplace transform of $M(t)$ also positive semidefinite? $$ \int_{t=0}^{\infty}e^{-s t} M(t) dt. $$ Here $s$ is a complex number.