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.....

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

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