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I have N samples of complex, correlated vectors (my data). I also have a model (a complex function with complex parameters) that I want to fit to the data.

If everything were real, I know what I need to do. I would just compute the covariance matrix

$\Sigma_{i,j}=(y_i-<y>_i)(y_j-<y>_j)$, ($y$ is a vector from a set of vectors)

invert it, then use some algorithm like Levenberg–Marquardt to minimize the my Chi-Squared function

Minimize $\chi^2 = (y_j-f(\vec{p},x_j))\Sigma_{j,i}^{-1}(y_i-f(\vec{p},x_i))/\text{D.O.F.}$ ($f$ is the model I am fitting to)

where $\vec{p}$ are the parameters I want.

My question is, how do I generalize this for complex $\vec{x}$, for complex parameters $\vec{p}$?

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