Complex-Valued Matrix Derivatives

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.

Spis treści:
Preface
Nomenclature
List of abbreviations
1. Introduction
2. Background material
3. Theory of complex-valued matrix derivatives
4. Development of complex-valued derivative formulas
5. Complex Hessian matrices for scalar, vector, and matrix functions
6. Generalized complex-valued matrix derivatives
7. Applications in signal processing and communications
References
Index.