Hjørungnes Are. Complex-Valued Matrix Derivatives With Applications in Signal Processing and Communications

Cambridge University Press, 2011. — 270 p. — ISBN10: 0521192641, ISBN13: 978-0521192644This book is written as an engineering-oriented mathematics book. It introduces the field involved in finding derivatives of complex-valued functions with respect to complexvalued matrices, in which the output of the function may be a scalar, a vector, or a matrix. The theory of complex-valued matrix derivatives, collected in this book, will benefit researchers and engineers working in fields such as signal processing and communications. Theories for finding complex-valued derivatives with respect to both complex-valued matrices with independent components and matrices that have certain dependencies among the components are developed and illustrative examples that show
howto find such derivatives are presented.Key results are summarized in tables. Through several research-related examples, it will be shown how complex-valued matrix derivatives can be used as a tool to solve research problems in the fields of signal processing and communications.