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My question is concerning how to compute the complex gradient of the following cost functional with respect to W (grad_w(F)):

F=Ʃ_i=1:M ||y_i-Go*W_i||^2 + Ʃ_i=1:M ||W_i - X*(E_i - Gc*W_i)||^2

Where the summations go from i=1 to i=M and the dimensions of the diferent elements are:

y: Nx1

Go: Nxn

W: nx1

X:nxn

E_i:nx1

Gc:nxn

And ||..||^ 2 indicates the square norm.

The elements of the different matrix and vectors are complex numbers

My problem is that I need to compute the gradient to apply a conjugate gradient minimization algorithm to minimize the cost functional. Any help or reference about how to compute gradients of this type of expressions (vectors and matrix) will be appreciated.

Thank you very much.

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# Complex gradient of a matrix expression

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