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Product details
File Size: 31759 KB
Print Length: 504 pages
Publisher: Wiley; 3 edition (February 19, 2019)
Publication Date: February 19, 2019
Sold by: Amazon Digital Services LLC
Language: English
ASIN: B07PS6Y6W6
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Amazon Best Sellers Rank:
#675,469 Paid in Kindle Store (See Top 100 Paid in Kindle Store)
Matrix differential Calculus is probably not something you might encounter everyday, but if you do then this is the book that will guide you through everything relevant thing that you need to know about it. The book is educational in the sense that it walks you through matrix theory and linear algebra and then advances into calculus and more advanced topics. However, what I also find very attractive about this book is that it can serve as a reference. Whenever you are held up by an issue, you just browse through the book and find some theorem or formula that quickly resolves the situation for you. So I would recommend that you a copy on your shelf to go to repeatedly.
I purchased it to prepare myself in order to take a PhD selection exam in Economics. The content is superb, unfortunately the type isn't good.
This book is a gem, not so much for the results it contains, but for how it presents them. The authors introduce a compact notation centered on kronecker products and schur products. In addition they present a useful set of operators and identities for manipulating these objects. The result is a pleasing language for mathematical manipulation avoiding to a large extent the "debauchery of indices" that pose a problem in many investigations. This presentation makes the price of the book almost worthwhile. The review of the properties of matrices is compact and reasonably complete. The applications are straightforward and competently presented.
The paperback is the 2nd Edition and the hardback the 1st Edition. There's a 3rd Edition available in electronic form. It was completely re-typeset.The mathematical writing in this book is truly beautiful. And I have no complaints about the new typesetting.There's a crystal-clear, just-the-facts review of matrices, linear algebra, the basics of metric topology for R^N, convexity, and differential calculus. They have beautiful, easy-to-follow proofs of the key theorems. The approach is very (abstract) algebraic and (metric) topological, which I like. They take a Taylor-series-based approach to differential calculus that's very enlightening, arguing for the primacy of differentials over derivatives (which lines up with what I'm seeing in statistical physics books like Leimkuhler and Reich's book on Hamiltonian simulation). Overall, the introductory material was perfect for someone like me who needed to brush up on my continuous math for statistics and optimization after 25 years focusing on discrete math in computer science.The book really picks up after the basics, going into derivatives of simple matrix operations and pretty quickly ramping up to matrix operations like eigenvalues. I haven't even gotten to the optimization and statistics part of the book yet. The latter is mostly in a frequentist, maximum-likelihood setting, which fits in with the chapters on optimization.
For some reason, in spite of its enormous utility, matrix differential calculus is oddly absent from standard courses in signal processing and control. The great strength of this text is its focus on the development of sufficient and necessary conditions for constrained/unconstrained minima/maxima. There are good examples regarding maximum likelihood estimation. There are also some useful results regarding the Kronecker product and commutator matrices. The chapter at the end covers specific topics in econometrics. The paperback edition suffers from completely hideous typesetting that is exacerbated by some of the notation. In spite of the fact that the paperback is not cheap, the pages look like they were photocopied. Maybe I just got a bad copy. I don't know if the hardback edition has the same problem.
I am unusually lucky to get around the typesetting problems described by other reviewers: I was translating the book into Russian a few years ago based on the authors' LaTeX files, so I am not even sure I saw the Wiley book printed. I also was able to receive the author copy from the Russian publisher for free. Of course Wiley's price of $300 is ridiculous! The authors complained about it, too, seeing this as an objective obstacle for dissemination, but there is little they could do about the price.I have not appreciated the book that much until I hit the need for matrix calculus for my dissertation research. Knowing the book fairly closely, I was able to find the results I needed in 15 minutes, and applying them to my problem provided a huge leap in the generality of results, as well as shortened the derivations from about 15 pages of ugly element by element computations to about three pages. Two thumbs up!The book also contains a wealth of important mathematical results and makes the reader think rigorously about their notation (which is important for both matrix computations and for caclulus, thus making it at least twice as important in matrix calculus), so it can be targeted not only at statistical and econometric audiences, but can also serve as a useful supplement to a linear algebra course.
I was surprised to learn about the poor quality of typesetting in the paperback (second?) edition. I reviewed the book for JASA, when it first appeared, and, over the years, I've used it many many times. It is really a remarkable book, for allof us who need to deal with matrices in our everyday research work.I was about to buy a second copy of the book, but the hardcover rice is ridiculous (more than $300!!), and I was turned away from buying the paperback edition because of the comments on the bad quality of typesetting.This is too bad. A book of this stature deserves a better treatment by the publisher!
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