Complex-Valued Matrix Derivatives

Erscheinungsjahr 2011
ISBN: 978-0-521-19264-4
Verlag: Cambridge University Press

Buch, Englisch, 270 Seiten, Format (B × H): 175 mm x 250 mm, Gewicht: 650 g

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.

Autoren/Hrsg.

Hjørungnes, Are

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Lineare und multilineare Algebra, Matrizentheorie
• Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure
• Mathematik | Informatik EDV | Informatik Informatik Bildsignalverarbeitung
• Technische Wissenschaften Elektronik | Nachrichtentechnik Nachrichten- und Kommunikationstechnik Signalverarbeitung
• Technische Wissenschaften Sonstige Technologien | Angewandte Technik Signalverarbeitung, Bildverarbeitung, Scanning
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik

Inhaltsverzeichnis

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.

Über Autor(innen)

Hjørungnes, Are
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.