A systematic theory is introduced for finding the derivatives of complex-valued matrix functions with respect to a complex-valued matrix variable and the complex conjugate of this variable. In the framework introduced, the differential of the complex-valued matrix function is used to identify the derivatives of this function. Matrix differentiation results are derived and summarized in tables which can be exploited in a wide range of signal processing related situations.
Complex-valued matrix differentiation: techniques and key results
IEEE Transactions on Signal Processing, Volume 55, N°6 Part I, June 2007
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