Suppose I have the following expression $$f(z)=Q +zS+\bar{z}S^\top + \bar{z}Rz$$ with $z\in \mathbb{C}$ and $Q,S,R$ are real matrices of suitable dimensions and $Q=Q^\top$, $R=R^\top$. I want to show that the above expression is convex, therefore I computed the double derivative with respect to $z$ to see if it is $>0$, but I'm not sure whether my derivative is correct or not. I computed $$f'(z)=S+S^\top + Rz+\bar{z}R$$ Is this correct? In particular, I am not sure about the derivative of $\bar{z}S^\top + \bar{z}Rz$
2026-04-04 02:12:44.1775268764
Derivative of complex expression
45 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in LINEAR-ALGEBRA
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