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


  • Date Published: March 2011
  • availability: In stock
  • format: Hardback
  • isbn: 9780521192644


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About the Authors
  • 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.

    • First self-contained book covering complex-valued matrix derivatives from an engineering perspective
    • Uses recent research examples from signal processing and communications to demonstrate how differentiation theory can be applied in practice
    • Contains over 80 end-of-chapter exercises, with a complete solutions manual available at
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    Reviews & endorsements

    "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

    "self-contained engineering approach to the study of derivatives.." - A. Bultheel, Mathematics Reviews

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    Product details

    • Date Published: March 2011
    • format: Hardback
    • isbn: 9780521192644
    • length: 270 pages
    • dimensions: 253 x 179 x 17 mm
    • weight: 0.69kg
    • contains: 10 b/w illus. 17 tables 81 exercises
    • availability: In stock
  • Table of Contents

    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

  • instructor resources

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    Instructor ResourcesSolutionsSolutions manualpdf424KB0solutions instructor resources solutions instructor resourcessolutions

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    These resources are provided free of charge by Cambridge University Press with permission of the author of the corresponding work, but are subject to copyright. You are permitted to view, print and download these resources for your own personal use only, provided any copyright lines on the resources are not removed or altered in any way. Any other use, including but not limited to distribution of the resources in modified form, or via electronic or other media, is strictly prohibited unless you have permission from the author of the corresponding work and provided you give appropriate acknowledgement of the source.

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  • Author

    Are Hjørungnes, University of Oslo
    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.

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