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.
Introduces a powerful set of mathematical tools that can be used to analyze and optimize the performance of engineering systems.
Are Hjørungnes is a Professor in the Faculty of Mathematics and Natural Sciences at the University of Oslo, Norway. He is an Editor of the IEEE Transactions on Wireless Communications and has served as a Guest Editor of the IEEE Journal of Selected Topics in Signal Processing and the IEEE Journal on Selected Areas in Communications.
'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)
'Complex vector and matrix optimization problems are often
encountered by researchers in the electrical engineering fields and
much beyond. Their solution, which can sometimes be reached from
using existing standard algebra literature, may however be a time
consuming and sometimes difficult process. This is particularly so
when complicated cost function and constraint expressions arise.
This book brings together several mathematical theories in a novel
manner to offer a beautifully unified and systematic methodology
for approaching such problems. It will no doubt be a great
companion to many researchers and engineers alike.' Professor David
Gesbert, EURECOM, Sophia-Antipolis, France
'… an excellent monograph … The book is suitable as a textbook in
graduate-level studies and research.' Zentralblatt MATH
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