So my thesis superviser is out of town for a whole month and won't let me contact him :/
He gave me this expression for the hessian matrix with complex variables (check out the photo) but there seems to be an issue here.
I am pretty sure that a pair of entries (maybe more?) are in the wrong spots. Entry (1,1) should be the complex conjugate of (2,2) and (1,2) should be the complex conj of (2,1) right?
Is there a way to get the correct expression with-out using different derivatives as shown in the photo? So for example, without using $\cfrac{d^2f}{d\theta^2}$.
Some extra info: $f$ is a matrix expression and I think the reason we want our hessian structured in this way is due to the fact that our gradient was extracted thru application of $\cfrac{d}{d\theta^*}$?
Not sure, this structure is kind of confusing, I would have thought we would have used
$$ \left[\begin{matrix} \cfrac{d^2}{d\theta^2} & \cfrac{d^2}{d\theta\,d(\theta^*)}\\ \cfrac{d^2}{d(\theta^*)\,d\theta} & \cfrac{d^2}{d(\theta^*)^2} \end{matrix}\right] $$
But I dont know why my supervisor doesn't use this structure.
Thank you all for taking the time! appreciate any help I can get.