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Matrix Algebra From a Statistician's Perspective [Paperback]

David A. Harville
4.5 out of 5 stars  See all reviews (15 customer reviews)

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Book Description

June 30, 2008 0387783563 978-0387783567 1st ed. 1997. 2nd printing 2008
A knowledge of matrix algebra is a prerequisite for the study of much of modern statistics, especially the areas of linear statistical models and multivariate statistics. This reference book provides the background in matrix algebra necessary to do research and understand the results in these areas. Essentially self-contained, the book is best-suited for a reader who has had some previous exposure to matrices. Solultions to the exercises are available in the author's "Matrix Algebra: Exercises and Solutions"

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Editorial Reviews


From a review:


"This is a book that will be welcomed by many statisticians at most stages of professional development. ...It is essentially a carefully sequenced and tightly interlocking collections of proofs in an elementary, though very pure mathematical style."


From the Publisher

A knowledge of matrix algebra is a prerequisite for the study of much of modern statistics, especially the areas of linear statistical models and multivariate statistics. This reference book provides the background in matrix algebra necessary to do research and understand the results in these areas.

* This book presents matrix algebra in a way that is well-suited for those with an interest in statistics or related disciplines * Includes a number of useful results that have previously only been available from relatively obscure sources * Detailed proofs are provided for all results * The style and level of presentation are designed to make the contents accessible to a broad audience --This text refers to the Hardcover edition.

Product Details

  • Paperback: 634 pages
  • Publisher: Springer; 1st ed. 1997. 2nd printing 2008 edition (June 30, 2008)
  • Language: English
  • ISBN-10: 0387783563
  • ISBN-13: 978-0387783567
  • Product Dimensions: 1.3 x 6.1 x 9.1 inches
  • Shipping Weight: 2 pounds (View shipping rates and policies)
  • Average Customer Review: 4.5 out of 5 stars  See all reviews (15 customer reviews)
  • Amazon Best Sellers Rank: #876,668 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews
18 of 18 people found the following review helpful
5.0 out of 5 stars Execllent reference, even for non-statisticians July 17, 2002
By A Customer
I am not a statistician, but this book has been my major reference on matrix algebra since I got it. The presentation is a bit dense, but I want to point out that the author actually presents the proofs to essentially _all_ theorems in the book. Perhaps this explains the style. As for the content, I find this book very comprehensive in my experience. But the dense page-setting of the book actually makes it visually challenging to locate a result. I also note that there are extensive exercises at the end of every chapter, although I probably won't use this as a textbook for my students.
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19 of 20 people found the following review helpful
5.0 out of 5 stars An excellent book on matrices October 3, 2000
By A Customer
This book is a true rarity. The exposition is very mathematical, and, therefore, many mathematicians (interested in matrix algebra) will find this book very useful and interesting. The exposition is clear, and quite complete. Of great interest are topics such as idempotent matrices, differentiation of matrices, invertibility.
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10 of 10 people found the following review helpful
Format:Paperback|Verified Purchase
Original review:
I'm currently using this book in a class I'm taking. Overall, the content of the book is very solid, and I can see keeping this book (or possibly the hardcover version) on my shelf for years to come. However, the material is very dense and the exposition is generally lacking. Reading this book is difficult due in part to the poor layout decisions that were made; the layout isn't atrocious, but there is significant room for improvement. Also, the soft-cover seems to not want to stay closed (just a minor annoyance).

If you've never taken a matrix algebra course before, this is not the book to learn from (try either the Hoffman and Kunze or Friedberg books - both are considered good undergraduate-level texts). If you are looking for a book to act as a reference, this is a good choice. In my opinion, there should be a somewhat larger focus on the applications of the matrix algebra to statistics.

(4 stars because it is a solid reference and I knew that is what it aims to be - it lost a star due to the layout and cover issues as well as the dissatisfying lack of direct applications to statistics).

As the semester progressed and the material covered in the book moved further from material I knew, I became more and more dissatisfied with it. Learning matrix algebra from this book would be like learning English from a dictionary. There are VERY few examples (asymptotically 0?) and very little explanation of what everything relates to.

Here is an example of exposition leading up to a theorem which I would say characterizes 90% of the book:
"The following theorem, which extends the results of Theorem 14.12.19, is obtained by combining the results of Theorem 14.12.32 with those of Theorem 14.12.26 and Corollary 14.12.27.
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17 of 20 people found the following review helpful
5.0 out of 5 stars Solid and understandable guide to matrix algebra September 23, 2005
I am a PhD level graduate student who has never had a matrix algebra course. I got this book to help with a Linear Models course I am currently taking. The book is very helpful, and provides a solid background in the first few chapters before building on them for more complex results. Definitely a good reference to have nearby.
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4 of 4 people found the following review helpful
Format:Hardcover|Verified Purchase
There are tons of books on linear algebra, but very few with the scope of this one. Researchers facing any non-trivial task in linear algebra would do well to look here first. There are, for example, chapters on how vectorizing matrices (by stacking the columns) relates to Kronecker products, and taking derivatives of matrix functions. If you need to take the derivative of the determinant of a matrix with respect to its inverse, look no further. I wish the book was typeset better, but the content is fantastic.
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3 of 3 people found the following review helpful
5.0 out of 5 stars Good general book on matrices January 23, 2010
Format:Paperback|Verified Purchase
It is difficult to find an advanced book on matrix algebra. In any discipline that requires numerical computation, one needs knowledge of advanced matrix algebra. Analytical matrix algebra does not have a natrual home. Almost all linear algebra books are too low of level. There are books on numerical linear algebra such as Trefethen and Bau or Golub and Van Loan and books on vector space linear algebra such as Hoffman and Kunze, but neither of these types of books provide broad coverage of advanced matrix algebra. This book fills that gap. I consider this book to be superior to Applied Matrix Algebra in the Statistical Sciences by Alexander Basilevsky, Matrix Algebra: Theory, Computations, and Applications in Statistics by Gentle, and A Matrix Handbook for Statisticians by Seber.

As one reviewer notes, the book does not have a lot of problems. I would focus more on proving the theorems rather than the number of problems. Harville could have proved less of the theorems, and inserted them as problems, but he proved a large number of theorems in detail.
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3 of 3 people found the following review helpful
4.0 out of 5 stars Great Reference but not Suitable for Learning November 29, 2008
The book is very dense and detailed, which makes it an excellent reference book. However, I don't believe this book is suitable for learning Matrix Algebra. Each chapter includes only a few practice problems which I found to be a major shortcoming. I still gave it a 4/5 because it will still be very helpful for me as a reference.
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2 of 2 people found the following review helpful
3.0 out of 5 stars Good Reference October 18, 2010
By Guy
Format:Hardcover|Verified Purchase
To get this out of the way first and foremost, this book simply WILL NOT STAY OPEN for at least the first 150 pages. I realize this isn't a real criticism about the material, but it is annoying enough to mention. I've never seen a hardcover book be this stubborn about staying on a page. I've tried everything from weighing it down with something reasonably heavy to stomping on the spine. As soon as I set it down, it closes.

---End Rant---

I was assigned this book for a matrix algebra course, the idea being to get incoming graduate students ready for linear models by patching up any holes in linear algebra. Towards that end, working through this book seems inefficient. It's supposed to be from a statistician's perspective, yet somehow eigenvalues/eigenvectors and the Spectral Theorem aren't touched until 21 chapters in. I find it a little odd that nullspaces aren't defined until 11 chapters in (most texts would address this by chapter 2 I think) and the closest thing to an application comes in chapter 12 with the discussion of projection matrices. I can't decide whether I like or dislike the fact that the book basically ignores computational aspects (e.g. you won't find anything about putting a matrix in reduced row echelon form in here, and very little discussion on, say, the practical ways to invert a matrix).

A unique aspect of this book, compared with other Linear Algebra texts, is the level of abstraction. Everything is at the level of the vector space R^(m x n), which I suppose allows for the discussion of more specialized topics without having to specify. In my opinion, it's pretty comprehensive at this level of generality and covers many topics that are omitted in more standard texts.
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Most Recent Customer Reviews
5.0 out of 5 stars Excellent Text Book for Statisticians and Researchers.
I chose this book because of a recommendation from my instructor. Explanations are exceptionally clear and well thought out. Read more
Published 15 months ago by Sherri A. Verdugo
4.0 out of 5 stars Great reference
This book is a must to have in your shelf if you deal more than once with matrices. Do not expect to learn from it as from a textbook but it is great as a reference - easy to find... Read more
Published on July 27, 2011 by Vladislavs Dovgalecs
5.0 out of 5 stars excellent overview of matrix algebra relevant to statistics
Linear models and multivariate statistics are fundamental topics in statistics. A good understanding of both requires a command of linear algebra. Read more
Published on April 17, 2011 by Sunny
5.0 out of 5 stars Deep treatment of the subject matter that should have been marketed...
This is a fantastic treatment of advanced matrix algebra that is applicable to many areas such as controls, econometrics, multi-variable stats, optimization, etc. Read more
Published on May 1, 2009 by sp
5.0 out of 5 stars A very good book
This book is a very comprehensive and useful book. This is going to be a companion to graduate students in statistics, econometrics, etc. Read more
Published on November 23, 2008 by Savvas Papadopoulos
5.0 out of 5 stars Good service
Buying from directly instead of from its markplace is a pleasent experience. It is safe and faster delivery. Highly recommend.
Published on September 26, 2005 by Y. Li
4.0 out of 5 stars Its a good tool book
This is a pretty good tool book for a statistician but it still has some samll problems, (1) the first few chapters, author should give more examples to describe concepts. Read more
Published on July 15, 2004
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