Complex-Valued Matrix Differentiation: Techniques and Key Results

  • Authors:
  • A. Hjorungnes;D. Gesbert

  • Affiliations:
  • UniK-Univ. Graduate Center, Oslo Univ.;-

  • Venue:
  • IEEE Transactions on Signal Processing
  • Year:
  • 2007

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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