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eBook Matrix Algebra From a Statistician's Perspective ePub

eBook Matrix Algebra From a Statistician's Perspective ePub

by David A. Harville

  • ISBN: 038794978X
  • Category: Mathematics
  • Subcategory: Math Science
  • Author: David A. Harville
  • Language: English
  • Publisher: Springer; Corrected edition (November 30, 2000)
  • Pages: 634
  • ePub book: 1150 kb
  • Fb2 book: 1164 kb
  • Other: docx lrf lit doc
  • Rating: 4.3
  • Votes: 631

Description

Learning matrix algebra from this book would be like learning English from a dictionary. It's supposed to be from a statistician's perspective, yet somehow tors and the Spectral Theorem aren't touched until 21 chapters in.

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 1. 2. 19, is obtained by combining the results of Theorem 1. 32 with those of Theorem 1. 26 and Corollary 1.

Matrix algebra plays a very important role in statistics and in many other dis- plines. In many areas of statistics, it has become routine to use matrix algebra in ederivationorveri?cationofresults. Onesuchareaislinear statistical models; another is multivariate analysis. In these areas, a knowledge of matrix algebra isneeded in applying important concepts, as well as instudying the underlying theory, and is even needed to use various software packages (if they are to be used with con?dence and competence)

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

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. Essentially self-contained, the book is best-suited for a reader who has had some previous exposure to matrices.

Start by marking Matrix Algebra From A Statistician's Perspective as Want to Read . It includes a number of very useful results This book presents matrix algebra in a way this is well suited for those with an interest in statistics or a related discipline.

Start by marking Matrix Algebra From A Statistician's Perspective as Want to Read: Want to Read savin. ant to Read. It provides thorough and unified coverage of the fundamental concepts along with the specialized topics encountered in areas of statistics, such as linear statistical models and multivariate analysis. Detailed proofs are provided for all results.

Perspective David A. Harville Matrix Algebra From a Statistician’s Perspective.

Matrix Algebra From a Statistician’s Perspective David A. Author: David A. Harville.

Basics of Matrix Algebra for Statistics with .

Basics of Matrix Algebra for Statistics with R. Book. Armed with the mathematical model of the snake robot presented earlier in this book, we attempt in this chapter to contribute to the understanding of snake robots by employing nonlinear system analysis tools for investigating fundamental properties of their dynamics. We will also derive several interesting properties of snake robot locomotion simply by investigating the equations of motion of the robot, some of which will be instrumental in the development of a simplified model later in this book

The exercises are taken from my earlier book Matrix Algebra From a Statistician's Perspective. This book comprises well over three-hundred exercises in matrix algebra and their solutions.

The exercises are taken from my earlier book Matrix Algebra From a Statistician's Perspective. They have been restated (as necessary) to make them comprehensible independently of their source. To further insure that the restated exercises have this stand-alone property, I have included in the front matter a section on terminology and another on notation. The exercises are taken from my earlier book Matrix Algebra From a Statistician's Perspective.

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."

Comments

Undeyn Undeyn
It's neither the greatest nor the worst book in the world. It's primarily a theorem-proof theorem-proof book, with very few examples. It's certainly not appropriate for an undergraduate course, and you should have at least taken a first course in linear algebra in order to understand most of it (but probably not all of it).

This book was assigned to use in a Matrix Algebra class I have for my PhD in statistics. It probably serves better as a reference text rather than a course text. I am sure there are better books out there.
invincible invincible
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.
Malalrajas Malalrajas
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.
Skyway Skyway
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.