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David A. Harville
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Matrix Algebra From a Statistician's Perspective ハードカバー – 1997/9/5

英語版 David A. Harville (著)
4.0 5つ星のうち4.0 14個の評価
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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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  1. 本の長さ
    634ページ
  2. 言語
    英語
  3. 出版社
    Springer
  4. 発売日
    1997/9/5
  5. 寸法
    16.51 x 3.81 x 24.77 cm
  6. ISBN-10
    038794978X
  7. ISBN-13
    978-0387949789
  8. すべての詳細を表示
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ページ 1 以下のうち 1 最初から観るページ 1 以下のうち 1
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  1. 統計のための行列代数 下
  2. Matrix Algebra: Exercises and Solutions
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商品の説明

内容説明

統計ユーザーが線形統計モデルや多変量解析での応用に必要とする線形代数の基礎を,具体的に行列を使って解き明かした入門書.原則として全ての定理に証明がついている.また,それぞれの理論の道筋の途中で読者がつまづきやすい箇所には,「どこがわかればわかるのか」を明らかにしつつ,「なぜそうなるのか」が懇切丁寧に解説されている.

出版社からのコメント

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

登録情報

  • 出版社 ‏ : ‎ Springer; 1st ed. 1997. Corr. 3rd printing 2000版 (1997/9/5)
  • 発売日 ‏ : ‎ 1997/9/5
  • 言語 ‏ : ‎ 英語
  • ハードカバー ‏ : ‎ 634ページ
  • ISBN-10 ‏ : ‎ 038794978X
  • ISBN-13 ‏ : ‎ 978-0387949789
  • 寸法 ‏ : ‎ 16.51 x 3.81 x 24.77 cm
  • カスタマーレビュー:
    4.0 5つ星のうち4.0 14個の評価

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David A. Harville

David A. Harville

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Ozzymandias
5つ星のうち2.0 Wading through obvious theorems and lemmas before getting to anything useful
2018年9月14日に英国でレビュー済み
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If you are looking for concise, practical text on matrix algebra, for goodness sake don't buy this book! Firstly though the book is very large, there's actually not very much in it. There are too many pages of lemmas and theorems you'll never need or are patently obvious, and practical it is not! Very formal and voluminous, and pretty thin in actual material.

The book claims to be from a statistician perspective, but if you are a student statistician you a need clear and concise text and this is not it! If you are a research statistician especially in this big data age, you need much more practical theory than this book offers.

In addition, it doesn't really make a good reference book because the material is not set out in a clear way, important theorems are buried with trivial theorems, so prepare to get your highlighter out and mark the pages!

Find a better book to buy!
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A Buyer
5つ星のうち5.0 Good general book on matrices
2010年1月23日にアメリカ合衆国でレビュー済み
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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.
8人のお客様がこれが役に立ったと考えています
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Douglas Whitaker
5つ星のうち2.0 Good reference book, not the book to learn matrix algebra from for the first time
2010年9月21日にアメリカ合衆国でレビュー済み
Amazonで購入
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).

Updated:
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."
That's it. No other commentary, explanation of the purpose of the theorem or why it is important or how it relates to anything else. No theorems are highlighted as being more important than any other.

Moreover, the typesetting in the book is among the worst I've seen in a textbook - it really is very difficult to read more than a single theorem and proof.

As such, I've changed my rating to 2 stars.
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Sherri A. O'Gorman
5つ星のうち5.0 Excellent Text Book for Statisticians and Researchers.
2013年3月23日にアメリカ合衆国でレビュー済み
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I chose this book because of a recommendation from my instructor. Explanations are exceptionally clear and well thought out. Matrix operations are related to statistical analysis...for anyone that does any type of statistical (linear or multivariate analysis)....this is a must have book. Interpreting results can be daunting but this book helps clear mysteries that may persist due to traditional methods of teaching stats at an undergraduate level. For a graduate level statistics class, data mining class, or artificial intelligence class....again a must have book.
4人のお客様がこれが役に立ったと考えています
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Guy
5つ星のうち3.0 Good Reference
2010年10月18日にアメリカ合衆国でレビュー済み
Amazonで購入
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. As far as the general writing of the book, I feel that a lot of the material is under motivated, which is fine for a reference but not good for an assigned textbook.

I imagine that I will keep this book as a reference, particularly for the less essential material. It's well organized and, for my needs, comprehensive enough.
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