Title :
Complex-Valued Matrix Differentiation: Techniques and Key Results
Author :
Hjorungnes, A. ; Gesbert, David
Author_Institution :
UniK-Univ. Graduate Center, Oslo Univ.
fDate :
6/1/2007 12:00:00 AM
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
Keywords :
matrix algebra; signal processing; complex conjugate; complex-valued matrix differentiation; complex-valued matrix function; signal processing; Broadband communication; Councils; Design engineering; Design optimization; Jacobian matrices; MIMO; Mobile communication; Signal processing; Signal processing algorithms; Wireless communication; Complex differentials; Jacobian; complex matrix derivatives; nonanalytical complex functions;
Journal_Title :
Signal Processing, IEEE Transactions on
DOI :
10.1109/TSP.2007.893762
