Are HjørungnesCambridge University Press, 2/24/2011EAN 9780521192644, ISBN10: 0521192641Hardcover, 270 pages, 24.7 x 17.4 x 1.7 cmLanguage: EnglishIn 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.PrefaceNomenclatureList of abbreviations1. Introduction2. Background material3. Theory of complex-valued matrix derivatives4. Development of complex-valued derivative formulas5. Complex Hessian matrices for scalar, vector, and matrix functions6. Generalized complex-valued matrix derivatives7. Applications in signal processing and communicationsReferencesIndex.'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)
