Complex-Valued Matrix Derivatives
Cambridge University Press, 2/24/2011
EAN 9780521192644, ISBN10: 0521192641
Hardcover, 270 pages, 24.7 x 17.4 x 1.7 cm
Language: English
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.
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.
'This book addresses the problem of complex-valued derivatives in a wide range of contexts. The mathematical presentation is rigorous but its structured and comprehensive presentation makes the information easily accessible. Clearly, it is an invaluable reference to researchers, professionals and students dealing with functions of complex-valued matrices that arise frequently in many different areas. Throughout the book the examples and exercises help the reader learn how to apply the results presented in the propositions, lemmas and theorems. In conclusion, this book provides a well organized, easy to read, authoritative and unique presentation that everyone looking to exploit complex functions should have available in their own shelves and libraries.' Professor Paulo S. R. Diniz, Federal University of Rio de Janeiro (UFRJ)