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I'm am trying to figure this out but no success. I would like to confirm how to obtain the derivative of the real or complex components (separately) of a given complex quantity. The problem is eigenvalue-related.

I currently do have the expression for the derivative of a complex eigenvalue "Lambda" with respect to "x", as follows:

Lambda' = transpose{V} * [K' - Lambda*M'] * {V}

where ' denotes derivative with respect to "x", "V" is the complex eigenvector associated to the complex eigenvalue "Lambda", "K" and "M" are complex stiffness and mass matrices, respectively (although they could be any other given quantities which depend on "x").

Now, since "Lambda" is expressed as A + iB, I would like to know if it's possible to calculate the derivatives of A and B (with respect to "x") separately. Since all the parameters involved are complex quantities, I suppose one cannot simply take the real/imaginary component from the result of the expression above.

Thank you for your attention.

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# Derivative of real or imaginary components (of a complex quantity)

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