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书籍英文名称：Complex-Valued_Matrix_Derivatives With Applications in Signal Processing and Communications重点讲述了复值矩阵求导方法在信号处理和通信中的应用。Complex-Valued Matrix DerivativesIn this complete introduction to the theory of finding derivatives of scalar-,vectorand matrix-valued functions in relation to complex matrix variables, Hjorungnesdescribes an essential set of mathematical tools for solving research problems whereunknown parameters are contained in complex-valued matrices. Self-contained and easyto follow, this singular reference uses numerous practical examples from signal processing and communications to demonstrate how these tools can be used to analyze andoptimize the performance of engineering systems. This is the first book on complexalued matrix derivatives from an engineering perspective. It covers both unpatternedand patterned matrices, uses the latest research examples to illustrate concepts, andincludes applications in a range of areas, such as wireless communications control theory, adaptive filtering, resource management, and digital signal processing. The bookincludes eighty-one end-of-chapter exercises and a complete solutions manual(availablen the Web)Are Hjorungnes is a Professor in the Faculty of Mathematics and Natural Sciences athe University of oslo, Norway. He is an editor of the IEEE Transactions on wirelessCommunications, and has served as a guest editor of the eee Journal of selected topicsin Signal Processing and the Ieee Journal on selected Areas in CommunicationsThis book addresses the problem of complex-valued derivatives in a wide range ofcontexts. The mathematical presentation is rigorous but its structured and comprehensivepresentation makes the information easily accessible. Clearly, it is an invaluable referenceto researchers professionals and students dealing with functions of complex-valuedmatrices that arise frequently in many different areas Throughout the book the examplesand 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 functionsshould have available in their own shelves and librariesProfessor Paulo s.R. Diniz, Federal University of rio de janeiroComplex vector and matrix optimization problems are often encountered by researchersin the electrical engineering fields and much beyond. Their solution, which can sometimes be reached from using existing standard algebra literature, may however be atime consuming and sometimes difficult process. this is particularly so when complicated cost function and constraint expressions arise. This book brings together severalmathematical theories in a novel manner to offer a beautifully unified and systematicnethodology for approaching such problems. It will no doubt be a great companion tmany researchers and engineers alikeProfessor David Gesbert, EURECOM, Sophia-Antipolis, franceComplex-Valued MatrixDerivativesith applications in Signal Processingand communicationsARE HJORUNGNESUniversity of oslo, NorwayCAMBRIDGEUNIVERSITY PRESSCAMBRIDGE UNIVERSITY PRESSCambridge, New York, Melbourne, Madrid, Cape Town,Singapore, Sao Paulo, Delhi, Tokyo, Mexico CityCambridge University PressThe Edinburgh Building, Cambridge CB2 8RU, UKPublished in the united states of america by cambridge university press new Yorkwww.cambridge.orgInformationonthistitlewww.cambridge.org/9780521192644o Cambridge University Press 2011This publication is in copyright. Subject to statutory exceptionand to the provisions of relevant collective licensing agreements,no reproduction of any part may take place without the writtenpermission of Cambridge University PressFirst published 2011Printed in the United Kingdom at the University Press, CambridgeA catalogue record for this publication is available from the british LibraryLibrary of Congress Cataloguing in Publication dataHjoComplex-Valued Matrix Derivatives: With Applications in Signal Processing and CommunicationsAre HjorungnesIncludes bibliographical references and indeIsBN978-0-521-19264-4( hardback)1. Matrix derivatives. 2. Systems engineering. 3. Signal processing- Mathematical models4. Telecommunication -Mathematical models. I. TitleTA347.D4H562011621.3822-dc222010046598isbn 978-0-521-19264-4 HardbackAdditionalresourcesforthispublicationatwww.cambridge.org/hjorungnesCambridge University Press has no responsibility for the persistence oraccuracy of URLs for external or third-party internet websites referred to inthis publication and does not guarantee that any content on such websites isor will remain, accurate or appropriateTo my parents, Tove and oddContentsPrefacepage xIacknowledgmentsAbbreviationsNomenclaturentroduction1.1 Introduction to the book1.2 Motivation for the book1.3 Brief Literature Summary4 Brief OutlineBackground Material2.1 Introduction2.2 Notation and classification of Complex variables and functions235666772.2. 1 Complex-Valued Variables2.2.2 Complex-Valued Functions2.3 Analytic versus Non-Analytic Functions2.4 Matrix-Related Definitions2.5 Useful Manipulation Formulas202.5.1 Moore-Penrose Inverse2.5.2 Trace Operator242.5.3 Kronecker and Hadamard Products2.5. 4 Complex Quadratic Forms292.5.5 Results for Finding generalized Matrix Derivatives2. 6 Exercises38Theory of Complex-Valued Matrix Derivatives433. 1 Introduction433.2 Complex differentials3. 2. 1 Procedure for Finding Complex Differentials3.2.2 Basic Complex Differential Properties3.2.3 Results Used to Identify First-and Second-Order Derivatives53Contents3.3 Derivative with Respect to Complex Matrices3.3. 1 Procedure for Finding Complex-Valued Matrix Derivatives3.4 Fundamental Results on Complex-Valued Matrix Derivatives3.4.1 Chain rule3.4.2 Scalar real-Valued Functions3.4.3 One Independent Input Matrix Variable643.5 ExercisesDevelopment of complex-Valued Derivative Formulas704.1 Introduction704.2 Complex-Valued Derivatives of Scalar Functions704. 2. 1 Complex-Valued Derivatives of f(z, z704.2.2 Complex-Valued Derivatives of f(z, 3)744.2.3 Complex-Valued Derivatives of f(Z, Z)764.3 Complex-Valued Derivatives of Vector Functions824.3.1 Complex-Valued Derivatives of f(z,z824.3.2 Complex -Valued Derivatives of f(z, z)824.3.3 Complex-Valued Derivatives of f(Z, Z)824.4 Complex-Valued Derivatives of Matrix Functions844.4.1 Complex-Valued Derivatives of F(z, z)844.4.2 Complex-Valued Derivatives of F(z, z854.4.3 Complex-Valued Derivatives of F(Z, Z)864.5 Exercises91Complex Hessian Matrices for Scalar, Vector, and Matrix Functionsntroduction955.2 Alternative Representations of Complex-Valued Matrix Variables965.2. 1 Complex-Valued Matrix Variables Z and Z965.2.2 Augmented Complex-Valued Matrix Variables Z975.3 Complex Hessian Matrices of Scalar Functions5.3.1 Complex Hessian Matrices of Scalar Functions Using Z and Z5.3.2 Complex Hessian Matrices of Scalar Functions Using Z1055.3. 3 Connections between Hessians When Using Two-MatrixVariable representations1075.4 Complex Hessian Matrices of Vector Functions1095.5 Complex hessian Matrices of Matrix Functions1125.5.1 Alternative Expression of Hessian Matrix of Matrix Function1175.5.2 Chain Rule for Complex Hessian Matrices1175.6 Examples of Finding Complex Hessian Matrices1185.6.1 Examples of Finding complex Hessian matrices ofScalar functions1185.6.2 Examples of Finding Complex Hessian Matrices ofVector functions
