# what is the hessian matrix of $f(W) = \sqrt{Tr(W A_0 W A_1)}$? Here, $W$, $A_0$ and $A_1$ are positive semidefinite matrices and hermitian

what is the hessian matrix of $f(W) = \sqrt{Tr(W A_0 W A_1)}$? Here, $W$, $A_0$ and $A_1$ are positive semidefinite matrices and hermitian.

For the time being, I obtain the derivative as $\frac{\partial f}{\partial W} = \frac{A_0^T W^T A_1^T + A_1^T W^T A_0^T}{2\sqrt{Tr(W A_0 W A_1)}}$. I want to know the next step.....

• this would be a better fit for Math.SE – Thoth Jun 28 '18 at 4:43
• also, take a look at this: en.wikipedia.org/wiki/… – Thoth Jun 28 '18 at 5:02