Matrix Derivatives
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Matrix Derivatives
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Author : Gerald Stanley Rogers
language : en
Publisher:
Release Date : 1980
Matrix Derivatives written by Gerald Stanley Rogers and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980 with Mathematics categories.
Generalized Vectorization Cross Products And Matrix Calculus
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Author : Darrell A. Turkington
language : en
Publisher: Cambridge University Press
Release Date : 2013-02-11
Generalized Vectorization Cross Products And Matrix Calculus written by Darrell A. Turkington and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-02-11 with Business & Economics categories.
This book presents the reader with new operators and matrices that arise in the area of matrix calculus. The properties of these mathematical concepts are investigated and linked with zero-one matrices such as the commutation matrix. Elimination and duplication matrices are revisited and partitioned into submatrices. Studying the properties of these submatrices facilitates achieving new results for the original matrices themselves. Different concepts of matrix derivatives are presented and transformation principles linking these concepts are obtained. One of these concepts is used to derive new matrix calculus results, some involving the new operators and others the derivatives of the operators themselves. The last chapter contains applications of matrix calculus, including optimization, differentiation of log-likelihood functions, iterative interpretations of maximum likelihood estimators and a Lagrangian multiplier test for endogeneity.
Matrix Derivatives
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Author : Gerald S. Rogers
language : en
Publisher:
Release Date : 1980
Matrix Derivatives written by Gerald S. Rogers and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980 with categories.
Complex Valued Matrix Derivatives
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Author : Are Hjørungnes
language : en
Publisher: Cambridge University Press
Release Date : 2011-02-24
Complex Valued Matrix Derivatives written by Are Hjørungnes and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-02-24 with Technology & Engineering categories.
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.
Complex Valued Matrix Derivatives
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Author : Are Hjrungnes
language : en
Publisher:
Release Date : 2011
Complex Valued Matrix Derivatives written by Are Hjrungnes and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Electronic books categories.
In this complete introduction to the theory of finding derivatives of scalar-, vector- and matrix-valued functions with respect to complex matrix variables, Hjrungnes 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"
Kronecker Products And Matrix Calculus With Applications
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Author : Alexander Graham
language : en
Publisher: Courier Dover Publications
Release Date : 2018-06-13
Kronecker Products And Matrix Calculus With Applications written by Alexander Graham and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-13 with Mathematics categories.
Enhanced by many worked examples, problems, and solutions, this in-depth text is suitable for undergraduates and presents a great deal of information previously only available in specialized and hard-to-find texts. 1981 edition.
Advanced Multivariate Statistics With Matrices
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Author : Tõnu Kollo
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-03-30
Advanced Multivariate Statistics With Matrices written by Tõnu Kollo and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-03-30 with Mathematics categories.
The book presents important tools and techniques for treating problems in m- ern multivariate statistics in a systematic way. The ambition is to indicate new directions as well as to present the classical part of multivariate statistical analysis in this framework. The book has been written for graduate students and statis- cians who are not afraid of matrix formalism. The goal is to provide them with a powerful toolkit for their research and to give necessary background and deeper knowledge for further studies in di?erent areas of multivariate statistics. It can also be useful for researchers in applied mathematics and for people working on data analysis and data mining who can ?nd useful methods and ideas for solving their problems. Ithasbeendesignedasatextbookforatwosemestergraduatecourseonmultiva- ate statistics. Such a course has been held at the Swedish Agricultural University in 2001/02. On the other hand, it can be used as material for series of shorter courses. In fact, Chapters 1 and 2 have been used for a graduate course ”Matrices in Statistics” at University of Tartu for the last few years, and Chapters 2 and 3 formed the material for the graduate course ”Multivariate Asymptotic Statistics” in spring 2002. An advanced course ”Multivariate Linear Models” may be based on Chapter 4. A lot of literature is available on multivariate statistical analysis written for di?- ent purposes and for people with di?erent interests, background and knowledge.
Matrix Methods And Fractional Calculus
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Author : Mathai Arak M
language : en
Publisher: World Scientific
Release Date : 2017-11-10
Matrix Methods And Fractional Calculus written by Mathai Arak M and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-10 with Mathematics categories.
Fractional calculus in terms of mathematics and statistics and its applications to problems in natural sciences is NOT yet part of university teaching curricula. This book is one attempt to provide an approach to include topics of fractional calculus into university curricula. Additionally the material is useful for people who do research work in the areas of special functions, fractional calculus, applications of fractional calculus, and mathematical statistics. Contents: PrefaceList of SymbolsVector/Matrix Derivatives and OptimizationJacobians of Matrix Transformations and Functions of Matrix ArgumentFractional Calculus and Special FunctionsFractional Calculus and Fractional Differential EquationsKober Fractional Calculus and Matrix-Variate FunctionsLie Theory and Special FunctionsSelected Topics in Multivariate Analysis Readership: Graduate students and researchers in all aspects of fractional calculus and its applications. Keywords: Vector/Matrix Derivatives;Optimization;Jacobians of Matrix Transformations;Multivariate Analysis;Functions of Matrix Argument;Fractional Calculus;Special Functions;Lie Theory;Fractional Differential Equations;Kober Fractional Calculus;Matrix-Variate FunctionsReview:0
Matrix Differential Calculus With Applications In Statistics And Econometrics
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Author : Jan R. Magnus
language : en
Publisher: John Wiley & Sons
Release Date : 2019-03-15
Matrix Differential Calculus With Applications In Statistics And Econometrics written by Jan R. Magnus and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-03-15 with Mathematics categories.
A brand new, fully updated edition of a popular classic on matrix differential calculus with applications in statistics and econometrics This exhaustive, self-contained book on matrix theory and matrix differential calculus provides a treatment of matrix calculus based on differentials and shows how easy it is to use this theory once you have mastered the technique. Jan Magnus, who, along with the late Heinz Neudecker, pioneered the theory, develops it further in this new edition and provides many examples along the way to support it. Matrix calculus has become an essential tool for quantitative methods in a large number of applications, ranging from social and behavioral sciences to econometrics. It is still relevant and used today in a wide range of subjects such as the biosciences and psychology. Matrix Differential Calculus with Applications in Statistics and Econometrics, Third Edition contains all of the essentials of multivariable calculus with an emphasis on the use of differentials. It starts by presenting a concise, yet thorough overview of matrix algebra, then goes on to develop the theory of differentials. The rest of the text combines the theory and application of matrix differential calculus, providing the practitioner and researcher with both a quick review and a detailed reference. Fulfills the need for an updated and unified treatment of matrix differential calculus Contains many new examples and exercises based on questions asked of the author over the years Covers new developments in field and features new applications Written by a leading expert and pioneer of the theory Part of the Wiley Series in Probability and Statistics Matrix Differential Calculus With Applications in Statistics and Econometrics Third Edition is an ideal text for graduate students and academics studying the subject, as well as for postgraduates and specialists working in biosciences and psychology.
Jacobians Of Matrix Transformations And Functions Of Matrix Argument
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Author : A. M. Mathai
language : en
Publisher: World Scientific
Release Date : 1997
Jacobians Of Matrix Transformations And Functions Of Matrix Argument written by A. M. Mathai and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Mathematics categories.
This book concentrates on the topic of evaluation of Jacobians in some specific linear as well as nonlinear matrix transformations, in the real and complex cases, which are widely applied in the statistical, physical, engineering, biological and social sciences. It aims to develop some techniques systematically so that anyone with a little exposure to multivariable calculus can easily follow the steps and understand the various methods by which the Jacobians in complicated matrix transformations are evaluated. The material is developed slowly, with lots of worked examples, aimed at self-study. Some exercises are also given, at the end of each section.The book is a valuable reference for statisticians, engineers, physicists, econometricians, applied mathematicians and people working in many other areas. It can be used for a one-semester graduate level course on Jacobians and functions of matrix argument.