Complex-Valued Matrix Derivatives : With Applications in Signal Processing and Communications

An introduction to a powerful set of mathematical tools for finding derivatives of scalar-, vector- and matrix-valued functions with respect to complex matrix variables. Self-contained and easy-to-follow, this singular reference uses numerous practical examples to demonstrate how these tools can be used to analyze and optimize performance of engineering systems.

In this complete introduction to the theory of finding derivatives of scalar-, vector- and matrix-valued functions with respect to complex matrix variables, Hjørungnes describes an essential set of mathematical tools for solving research problems where unknown parameters are contained in complex-valued matrices. The first book examining complex-valued matrix derivatives from an engineering perspective, it uses numerous practical examples from signal processing and communications to demonstrate how these tools can be used to analyze and optimize the performance of engineering systems. Covering un-patterned and certain patterned matrices, this self-contained and easy-to-follow reference deals with applications in a range of areas including wireless communications, control theory, adaptive filtering, resource management and digital signal processing. Over 80 end-of-chapter exercises are provided, with a complete solutions manual available online.