Complex-Valued Matrix Differentiation: Techniques and Key Results

Abstract

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