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Informationen zum Autor JAN R. MAGNUS is Emeritus Professor at the Department of Econometrics & Operations Research, Tilburg University, and Extraordinary Professor at the Department of Econometrics & Operations Research, Vrije University, Amsterdam. He is research fellow of CentER and the Tinbergen Institute. He has co-authored nine books and is the author of over 100 scientific papers. HEINZ NEUDECKER (1933-2017) was Professor of Econometrics at the University of Amsterdam from 1972 until his retirement in 1998. Klappentext 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. Inhaltsverzeichnis Preface xiii Part One - Matrices 1 Basic properties of vectors and matrices 3 1 Introduction 3 2 Sets 3 3 Matrices: addition and multiplication 4 4 The transpose of a matrix 6 5 Square matrices 6 6 Linear forms and quadratic forms 7 7 The rank of a matrix 9 8 The inverse 10 9 The determinant 10 10 The trace 11 11 Partitioned matrices 12 12 Complex matrices 14 13 Eigenvalues and eigenvectors 14 14 Schur's decomposition theorem 17 15 The Jordan decomposition 18 16 The singular-value decomposition 20 17 Further results concerning eigenvalues 20 18 Positive (semi)definite matrices 23 19 Three further results for positive definite matrices 25 20 A useful result 26 21 Symmetric matrix functions 27 Miscellaneous exercises 28 Bibliographical notes 30 2 Kronecker products, vec operator, and Moore-Penrose inverse 31 1 Introduction 31 2 The Kronecker product 31 3 Eigenvalues of a Kronecker product 33 4 The vec operator 34 5 The Moore-Penrose (MP) inverse 36 6 Existence and uniqueness of the MP inverse 37 7 Some properties of the MP inverse 38 8 Further properties 39 9 The solution of linear equation systems 41 Miscellaneous exercises ...
