Title :
Unified Theory of Complex-Valued Matrix Differentiation
Author :
Hjorungnes, A. ; Gesbert, David ; Palomar, Daniel P.
Author_Institution :
UniK-Graduate Center Univ., Oslo Univ., Norway
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 developed for use in signal processing and communications applications. Several other examples are given.
Keywords :
differentiation; matrix algebra; signal processing; telecommunication; communications; complex conjugate; complex-valued matrix differentiation unified theory; complex-valued matrix function derivatives; signal processing; Covariance matrix; Design engineering; Design optimization; Equalizers; Filters; MIMO; Mobile communication; Optimization methods; Signal processing; Vectors; Adaptive filters; Gradient methods; Linear algebra; Optimization methods;
Conference_Titel :
Acoustics, Speech and Signal Processing, 2007. ICASSP 2007. IEEE International Conference on
Conference_Location :
Honolulu, HI
Print_ISBN :
1-4244-0727-3
DOI :
10.1109/ICASSP.2007.366543
