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Matrix Algebra (Econometric Exercises, Vol. 1), by Karim M. Abadir, Jan R. Magnus
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The first volume of the Econometric Exercises Series, Matrix Algebra contains exercises relating to course material in matrix algebra that students are expected to know while enrolled in an (advanced) undegraduate or a postgraduate course in econometrics or statistics. The book features a comprehensive collection of exercises with complete answers. More than just a collection of exercises, the volume is a textbook organized in a completely different manner than the usual textbook. It can be used as a self-contained course in matrix algebra or as a supplementary text.
- Sales Rank: #1467081 in Books
- Brand: Brand: Cambridge University Press
- Published on: 2005-08-22
- Original language: English
- Number of items: 1
- Dimensions: 8.98" h x .94" w x 5.98" l, 1.68 pounds
- Binding: Paperback
- 466 pages
- Used Book in Good Condition
Review
"This collection of exercises in matrix algebra is useful as a text or a reference. It is clearly written and very thorough in its coverage of results used in econometrics. Besides basic topics, it has an excellent treatment of matrix inequalities, vectorization, and matrix calculus. It belongs on every econometrician's bookshelf." -Peter Schmidt, Michigan State University
About the Author
Karim Abadir has held a joint Chair since 1996 in the Department of Mathematics and Economics at the University of York, where he has been the founder and director of various degree programs. He has also taught at the American University in Cairo, the University of Oxford, and the University of Exeter. He became an Extramural Fellow at CentER (Tilburg University) in 1993. Professor Abadir is a holder of two Econometric Theory awards, and has authored many articles in top journals, including the Annals of Statistics, Econometric Theory, Econometrica, and the Journal of Physics. He is Coordinating Editor (and one of the founding editors) of the Econometrics Journal, and Associate Editor of Econometric Reviews, Econometric Theory, Journal of Financial Econometrics, and Portuguese Economic Journal. He is a Fellow of the Royal Statistical Society.
Jan Magnus is Professor of Econometrics, CentER and Department of Econometrics and Operations Research, Tilburg University, The Netherlands. He has also taught at the University of Amsterdam, The University of British Columbia, The London School of Economics, The University of Montreal, and The European University Institute among other places. His books include Matrix Differential Calculus (with H. Neudecker), Linear Structures, Methodology and Tacit Knowledge (with M. S. Morgan), and Econometrics: A First Course (in Russian with P. K. Katyshev and A. A. Peresetsky). Professor Magnus has written numerous articles in the leading journals, including Econometrica, The Annals of Statistics, The Journal of the American Statistical Association, Journal of Econometrics, Linear Algebra and Its Applications, and The Review of Income and Wealth. He is a Fellow of the Journal of Econometrics, holder of the Econometric Theory Award, and associate editor of The Journal of Economic Methodology, Computational Statistics and Data Analysis, and the Journal of Multivariate Analysis.
Most helpful customer reviews
0 of 0 people found the following review helpful.
fantastic reference book for engineering researchers
By Shag84
I have found this book invaluable in my dissertation in communications theory, which has some detailed linear algebra work. While Horn and Johnson's book is considered the linear algebra bible, many of the results in that book are more geared towards mathematicians. This book, on the other hand, has many results that are excellent for engineering. The book is laid out in a straightforward fashion, and I have found it easy to navigate the results. This book is a spectacular addition to the library of anyone working with applied linear algebra.
12 of 12 people found the following review helpful.
An excellent summary of many weird matrix results
By Stanislav Kolenikov
I have used this book as the source of inspiration for the introductory/background part of my doctorate level multivariate class when I was covering the foundations of matrix theory, this way and out. MANOVA and discriminant analysis are about the spectrum of W^{-1} B -- here are exercises on inverses, spectral decomposition, and traces. Marginal and conditional distributions of a multivariate normal are themselves normal -- here are block matrix results for inverses and such that those normality theorems are based on. Effects of non-normality come from the higher order moments -- here are Kronecker products to define those moments, and duplication matrices to deal with redundant elements. You want to see the effects of non-normality on your PCA or SEM procedures -- here are the matrix calculus results, the foundations of the matrix version of the delta method.
I won't be repeating the coverage of the book -- you can look at the Contents. What follows the Contents in the book is the list of exercises -- if you remember what it is that you want to find by name (Schur's inequality... 3x3 block inverse... determinant of the bordered Gramian...) you might be able to do that from that list. So the second use of the book beside the obvious source of homework, practice and test problems is a reference on the interesting results in matrix theory -- and not just the plain vanilla matrix algebra as one probably had had in their undergraduate courses (linear spaces, bases, ranks, linear systems, determinants, inverses -- and there's relatively not that much of it, as other books will have that covered in greater detail), but with all the stuff that one would need for serious multivariate research -- matrix calculus, vectorizations and Kronecker products, factorizations, commutation and duplication matrices. It was a savior for my research work time with those advanced results a couple of times.
Highly recommended for:
* any teacher of a graduate level course that involves serious matrix operations (advanced linear models, advanced multivariate statistics; the authors come from econometric tradition, so there must be some advanced econometric classes where that would be an important book, although I would probably see this stuff scattered over several courses, as far as I understand the typical econometric sequences);
* any researcher developing multivariate techniques that are heavily matrix-based. I work in structural equation modeling, and I've also found uses of matrix calculus in my earlier work in spatial statistics, although mostly based on earlier Jan Magnus' book with Heinz Neudecker, Matrix Calculus, that I was translating to Russian at some point in my life. Another suggested book specifically for multivariate results in matrix forms, in the most abstract ways, is Kollo and von Rosen, Advanced Multivariate Statistics with Matrices.
1 of 13 people found the following review helpful.
a good book
By Qu Feng
I think this book is a good reference book for the matrix tools used in econometrics.
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