Laplace transform of a time varying positive semidefinite matrix

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.

• positive semidefinite for all values of $s$? Including zero? If positive definite the integral would blow up for real negative $s$? – percusse Jun 7 '18 at 21:33
• No, only for those values of $s$ for which the Laplace transform makes sense. – K. Ghusinga Jun 8 '18 at 3:23