Lie Algebras in Particle Physics (Frontiers in Physics)

Book Description

An exciting new edition of a classic text

Howard Georgi is the co-inventor (with Sheldon Glashow) of the SU(5) theory. This extensively revised and updated edition of his classic text makes the theory of Lie groups accessible to graduate students, while offering a perspective on the way in which knowledge of such groups can provide an insight into the development of unified theories of strong, weak, and electromagnetic interactions.

Customer Reviews:

classical.......2005-08-05

very well written text about the algebra of standard model,
but not for beginers,a very solid background in particle physics
and symmetry methods for physics is required

A good *first* start.......2003-08-14

This book is good for what it is, namely, something to get your feet wet. When learning the basics of particle physics, e.g. as an undergrad or a beginning experimentalist, this is the quickest way to get a feel for the standard model gauge group.
However, this is *not* a complete text on group theory in particle physics (and therefore, little of what you need for supersymmetric field theories and string theories). So in addition to this book, you'd need something else with an introduction to the other things you need for your particular interest. Try Gilmore's "Applications of Lie algebras...", which I believe is out of print (in libraries). Also, Cornwell's abridged "Group theory in physics" is good (though if you can find the older set of three volumes, that may be more suited to your desires).
I don't suggest many of the other books on group theory for particles/fields/strings. There are tidbits of group theory you can pick up in the particular text you are working with, e.g. "Quantum theory of Fields" by Weinberg if you are learning quantum field theory.
For mathematical physics in general, I strongly suggest "Gauge fields, knots, and gravity" (John Baez), "Differential Geometry for physicists" (Chris Isham), and "Mathematical Physics" (Geroch).

What do you need more?.......2003-02-11

I'd say that, at least, the Georgi's book is too underestimated here.

I agree that this book lacks some notions and concepts which are usually dealt with in the matmatical literature, but not on logical clearity. Every book has its own way. For example the later parts of Green, Schwarz and Witten are also a mere sketches but it sufficiently pinpoints every important steps. A physically inclined reader(?), soon realize that it is filled with (and you may feel the leakage of) the master's intuition. You can see what mathematics going on beneath the physics. It is a well-framed series of informal lectures which reveals some space-between-lines secret.

good supplement.......2002-03-09

good supplement of introductory quantum field theory. particle physics books often have aggressiveness but this is in a relaxed mood, apt for reading in fine sunday mornings. 27 chapters in 300 pages, short chapters, without one for manifold and topology. from this book you can't get a mathematically deep understanding of Lie algebra nor exotic viewpoint for particle/string, but that's not this is for. i hope someday this will be included in Dover classics.

1.finite groups 2.Lie groups 3.SU(2) 4.tensor operators 5.isospin 6.roots and weights 7.SU(3) 8.simple roots 9.more SU(3) 10.tensor methods 11.hypercharge and strangeness 12.Young tableaux 13.SU(n) 14.3-d harmonic oscillator 15.SU(6) and the quark model 16.color 17.constituent quarks 18.unified theories and SU(5) 19.classical groups 20.classification theorem 21.SO(2n+1)and spinors 22.SO(2n+2)spinors 23.SU(n) Mediocre.......2001-09-01

Georgi's book has its strengths and weaknesses. It is very strong on application to physics but suffers greatly from a lack of mathematical substance. It has all the earmarks of a mathematics book written by a physicist: lots of physical insight but poor logical structure. Clear definitions and statements of theorems are missing and contribute to the nebulous feel of the text.

This is the kind of book that a casual reader will go through and think he has learned alot but for which the serious student who seeks a precise, thorough understanding of the material will likely end up confused at many points. It is a book of tools. The reader will not obtain a mastery of the subject but must suppliment this book with other, more theoretical treatments of representation theory.

Book Description

The best-selling, best known text in Mathematical Economics course, Chiang teaches the basic mathematical methods indispensable for understanding current economic literature. the book's patient explanations are written in an informal, non-intimidating style. To underscore the relevance of mathematics to economics, the author allows the economist's analytical needs to motivate the study of related mathematical techniques; he then illustrates these techniques with appropriate economics models. Graphic illustrations often visually reinforce algebraic results. Many exercise problems serve as drills and help bolster student confidence. These major types of economic analysis are covered: statics, comparative statics, optimization problems, dynamics, and mathematical programming. These mathematical methods are introduced: matrix algebra, differential and integral calculus, differential equations, difference equations, and convex sets.

Customer Reviews:

Great introduction to mathematical economics!.......2007-07-18

I enjoy Chiang's writing style. I've been reading up on mathematical methods in preparation for a masters econ program, and feel very comfortable with the material thanks to this textbook. The international edition is a good bargain.

A must read text book for any economics undergrad student.......2006-04-02

I found it extremely easy to read and at the same time rigorous enough to settle the bases. The author knows very deeply the economics students needs of mathematical methods and achieves a precise and complete explanation of all notions I needed to know for my undergrad course. I strongly recommend it during the first or second year.

A must read for graduate students in economics.......2006-02-26

Alpha Chiang's text should serve as the foundation for all quantitive analysis done in economic theory. It is an invaluable teaching tool for graduate students in economics and will help them better understand the mathematical techniques that have become so necessary for economic modeling.

I am not a highly quantitative person myself, but I found Chiang's book comprehensible and a useful reference guide in my gradaute economics classes. Along with Hal Varian's "Microeconomic Theory" and Jan Kmenta's "Econometrics", I would say that Chiang's "Fundamentals of Mathematical Economics" should serve as sacred literature for any prospective graduate student in economics.

not so good.......2005-10-14

the text carries to excess the concept of "keeping the presentation as simple as possible". but in general you cannot understand or solve problems with a fifth grader's ability to abstract them.
especially the relunctance to use matrix notation makes some topics actually harder to understand once they become more complicated.
furthermore I find the structure quite confusing since the text amounts to a monotous blabla - clear definitions might be helpful and some rigor would keep the reader conscious instead of drifting off. after all the text is not so bad but I think we deserve something better. blume might be better.

The best math textbook for economist.......2005-09-30

That is why it used everywhere, in nearly all economic departments. I strongly recommend you buy this book. It really helped me in my undergrad, and it is helping in my graduate courses. If you want to buy another book to accompany this, get Simon and Blume book. One person (probably little masochistic) was saying that Chiang has so many examples, blah, blah, blah. Look, not everyone is a math genius, undergraduate student's need Chiang, it's even useful for graduates. Math is used quite too excessively in economics...showing off?

Average customer rating:

worth the buy!
very useful for computations
Not for the uninitiated
An encyclopedic reference for matrix analysis and linear alg
Excellent book.... for the initiated

Matrix Analysis
Roger A. Horn , and Charles R. Johnson
Manufacturer: Cambridge University Press
ProductGroup: Book
Binding: Paperback

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ASIN: 0521386322

Book Description

Linear algebra and matrix theory have long been fundamental tools in mathematical disciplines as well as fertile fields for research. In this book the authors present classical and recent results of matrix analysis that have proved to be important to applied mathematics. Facts about matrices, beyond those found in an elementary linear algebra course, are needed to understand virtually any area of mathematical science, but the necessary material has appeared only sporadically in the literature and in university curricula. As interest in applied mathematics has grown, the need for a text and reference offering a broad selection of topics in matrix theory has become apparent, and this book meets that need. This volume reflects two concurrent views of matrix analysis. First, it encompasses topics in linear algebra that have arisen out of the needs of mathematical analysis. Second, it is an approach to real and complex linear algebraic problems that does not hesitate to use notions from analysis. Both views are reflected in its choice and treatment of topics.

Customer Reviews:

worth the buy!.......2007-06-30

THis book covers some key aspects in matrix analysis.

Would certainly recommend this book.

very useful for computations.......2007-01-13

I agree with other commentators who remarked that the book is better suited for someone already versed in linear algebra. For the student new to all this, the text can be, shall we say, too formidable?

A good usage is when you have studied the subject, perhaps several years ago, and need a concise refresher.

The strong aspect of the book is the emphasis on numerical calculations. Rather than about proving theorems. Don't worry that it was printed in 1990! While computers have heavily improved, thanks to Moore's Law, the maths of course has not. All the algorithms explained here are still germane to number crunching of linear systems. As another take, look at the Amazon page for the book, for the section about other books that cite this one. Notice the preponderance of computational books.

Not for the uninitiated.......2000-09-06

I bought this book hoping to learn about matrix analyis. I did not. This book is simply a reference manual with plenty of theorems, axioms etc. with little explanation. They give it to you rough and row. NOT A SINGLE SOLVED EXAMPLE, and not even solutions for the exercises given in the book are provided. If you intend to learn about matrix analysis, as I did, let not the 5 stars review mislead you. Don't make the same mistake, this book is not for you.

An encyclopedic reference for matrix analysis and linear alg.......2000-08-28

Horn and Johnson's MATRIX ANALYSIS is simply a masterpiece. You can find each and every result in matrix analysis along with it's proof in this book. Look at their companion volume "Topics in Matrix Analysis" too. Some of these results cannot be found elsewhere.

Excellent book.... for the initiated.......2000-07-09

Horn and Johnson has written an excellent reference book on somewhat-advanced linear algebra (from the point of view of an engineer). There's a lot of treasures in this book, but this book is NOT for beginning linear algebra. Rather, it is written as a handy reference to review and learn certain topics in linear algebra.

Nonetheless, I really like their take on linear algebra. They motivate you in every subject and problem (for example, the relations between eigenvectors, eigenvalues, and optimization problems). These insights are invaluable and definitely worth the admission price.

Book Description

Revised and updated, the third edition of Golub and Van Loan's classic text in computer science provides essential information about the mathematical background and algorithmic skills required for the production of numerical software. This new edition includes thoroughly revised chapters on matrix multiplication problems and parallel matrix computations, expanded treatment of CS decomposition, an updated overview of floating point arithmetic, a more accurate rendition of the modified Gram-Schmidt process, and new material devoted to GMRES, QMR, and other methods designed to handle the sparse unsymmetric linear system problem.

Customer Reviews:

Matrix Computations is an excellent guide to understanding and implementing Numerical Linear Algebra.......2007-09-30

This book is an excellent book for the student or researcher who needs to understand clearly the issues that arise in the developement of algorithms for the solution and analysis of linear systems. It gives a great explanation of how one operation like solving a linear system or doing just forward or backward solves can be mapped to basic BLAS primitives and how these variations have been implemented in popular libraries such as Lapack or BLAS and the archetectual reasons why one approach may be more optimized than another, row versus column operations, for example.

For the student it provides a nice walk through on the develpment of these algorithms and for the researcher provides a life long resource for reference to the many algorithms that are laid out here.

This book is clear and easy to follow and it is recomended for anyone who is serious about learning how to design and implement efficient linear algebra algorithms for a variety of archetectual and coding language environments.

bible.......2007-09-24

This book is a bible in matrix computation. While they have a lot of details on everything, though, the notations are rather complicated and hard-to-follow.

Gargantuan Copy and Paste Monument.......2007-05-07

Three stars are for:

(1) Relatively cheap price.
(2) Comprehensive but shallow coverage.
(3) Mass availability.

Hypothesis: The only three prematurely worn keys in Golub & Van Loan's keyboards must be: Control, C and V, since these form the shortcut for copy and paste operations.

There is no depth in this book when compared to classic matrix theory books, although I understand that this may distract from the possible use of the book as a reference manual. But as written, it is of little value in addition to Numerical Recipes; the latter has at least decent text this one does not have character, too much copying and pasting eliminated the book to form a skeleton.

What are the basis books for comparison?

1. Wilkinson, Algebraic Eigenvalue Problem. Super but expensive (>$100).
2. Marcus & Minc, A survey of Matrix Theory and Matrix Inequalities. Super but inexpensive (10$).
3. Horn and Johnson, Matrix Analysis, comprehensive, pretty good, and similarly priced to this ($30).

I am not suggesting that the content should mirror these books but the quality and depth should but despite being in its third edition, the book is full of errors both in pseudo-code and text.

The CTRL-C/CTRL-V effort is so insane that authors' could not help themselves to copy Wilkinson's theorem presentation sequence about the symmetric eigenvalue problem, but Wilkinson's commentary from his book (see Hoffman-Wielandt theorem in Golub & VanLoan second edition).

Whenever someone tells me that they learned something from Golub and Van Loan, I can not help myself to question what they thought they might have learned.

In almost all cases, Golub and Van Loan fans appear to know of a result through memorization without any clue about how it is derived and why it is important. So if this is your bible, then probably you do not deserve a job that requires critical thinking.

The books popularity tells something about the state of the academia: for example, the hotshots of signal processing republished Golub and Van Loan a few times to get their IEEE Fellow titles. Google for 'Multistage Wiener Filter', 'Relationship Conjugate Gradient MSWNF', 'Procrustes Rotations ESPRIT'. Definitely a field that does not appreciate critical thinking but fast copy and paste effort through graduate student slavery.

Exactly what I needed.......2007-03-08

I have been using "canned" programs for matrix calculations, but I needed to learn how they actaully work. This book provided exactly the information that I needed. This book is not for beginners--it requires a pretty good knowledge of linear algebra, but if you have that, this book will be most helpful in understanding sophisticated computational methods

The bible of numerical linear algebra.......2007-01-01

This book is the standard reference for all numerical linear algebra. It is a graduate-level applied math textbook written by practicing professionals for practicing professionals. If you are new to the topic you would probably prefer something like James Demmel's Applied Numerical Linear Algebra.

If you are interested in implementing the algorithms in this book, stop right now and first make sure that you can't use MATLAB or LAPACK instead, or even ScaLAPACK if you need a parallel implementation. Getting these algorithms right is hard, and the hard work has probably already been done by somebody else. LAPACK contains the accumulated wisdom of over forty years of research in numerical linear algebra, and MATLAB contains LAPACK. Don't re-invent the wheel.

On the other hand, if you want to understand how LAPACK works, or if you need to understand its numerical accuracy and stability, then this is the book for you.

Another reviewer has mentioned that this book contains numerous errata in the formulas. This is still true as of the third edition. Usually it is possible to detect and correct these errors by reading and understanding the surrounding text, but beware.

Matrix Analysis and Applied Linear Algebra Book and Solutions Manual

Average customer rating:

Progresses Well - Used for Self Study
Matrix Analysis and Applied Linear Algebra
A Model of Authorship
Beautiful Scaffolding
One of the best introductory (modern) books I know.

Matrix Analysis and Applied Linear Algebra Book and Solutions Manual
Carl Meyer
Manufacturer: SIAM: Society for Industrial and Applied Mathematics
ProductGroup: Book
Binding: Hardcover

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ASIN: 0898714540

Book Description

This book avoids the traditional definition-theorem-proof format; instead a fresh approach introduces a variety of problems and examples all in a clear and informal style. The in-depth focus on applications separates this book from others, and helps students to see how linear algebra can be applied to real-life situations. Some of the more contemporary topics of applied linear algebra are included here which are not normally found in undergraduate textbooks. Theoretical developments are always accompanied with detailed examples, and each section ends with a number of exercises from which students can gain further insight. Moreover, the inclusion of historical information provides personal insights into the mathematicians who developed this subject. The textbook contains numerous examples and exercises, historical notes, and comments on numerical performance and the possible pitfalls of algorithms. Solutions to all of the exercises are provided, as well as a CD-ROM containing a searchable copy of the textbook.

Customer Reviews:

Progresses Well - Used for Self Study.......2007-07-18

I self studied this book to improve my applied math skills. The book progresses well, with examples clear and easy to follow, even for a non mathematician such as myself. My background is only through the Calculus level. The book begins with linear equations then moves to matrix algebra, a logical approach. The author balances nicely what he refers to as "scaffolding" and the inherent efficiency of the topic.

With the exercises, I focused on the steps required to reach an accurate result and how I may apply this to the business I'm in and used Mathematica for many of the interim computations. This approach worked well for me and allowed me to better understand the topic as a whole, though it's doubtful I could have gotten away with this approach had I been in a formal classroom.

Matrix Analysis and Applied Linear Algebra.......2006-11-11

The book is ok. But It has A lot oF math proof and Word problems

A Model of Authorship.......2006-11-10

This book contains a comprehensive treatment on the topic of matrix analysis and applied linear algebra. The concepts are clearly introduced and developed. It is rich with detailed proofs that are easy to follow. Results are summarized and clearly grouped and marked for reference. As a researcher and a practitioner, I found this book quite useful in explaining mathematical concepts without the need for a classroom instructor.

Besides, this book comes with a CD that contains a PDF version which makes it quite useful to port as a reference. It is very rich with problem sets that add insight, both theoretically and practically. It is accompanied by a solutions manual which strengthens comprehension.

I highly recommend this book. I think it deserves to be a model to follow for authorship in the digital age.

Beautiful Scaffolding.......2006-08-09

Linear algebra is the Babel language of sciences, this book helps you to get proficient in speaking it. Clear-cut presentation, mathematical rigor and historical gossip is in such an unison, that you'll crave for a sequel. This is the 18-th 5-star rating, you shouldn't hesitate any more!

One of the best introductory (modern) books I know........2006-04-27

If you need to learn Linear Algebra and Matrix Theory, your best starting point is this book.

Very well written, many examples, and many "modern" results, that are not found in classics as Gantmacher (also an excellent book).

Buy it and see for yourself.

Average customer rating:

the sequel to "Matrix Analysis"
A great reference source for advanced matrix analysis

Topics in Matrix Analysis
Roger A. Horn , and Charles R. Johnson
Manufacturer: Cambridge University Press
ProductGroup: Book
Binding: Paperback

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ASIN: 0521467136

Book Description

Building on the foundations of its predecessor volume, Matrix Analysis, this book treats in detail several topics with important applications and of special mathematical interest in matrix theory not included in the previous text. These topics include the field of values, stable matrices and inertia, singular values, matrix equations and Kronecker products, Hadamard products, and matrices and functions. The authors assume a background in elementary linear algebra and knowledge of rudimentary analytical concepts. The book should be welcomed by graduate students and researchers in a variety of mathematical fields both as an advanced text and as a modern reference work.

Customer Reviews:

the sequel to "Matrix Analysis".......2007-01-15

This book is a sequel to, and a worthy successor of, "Matrix Analysis". The latter was directed mostly at methods applicable to solving generic matrix problems. Whereas the present book takes a more focused view. Its topics should be understood as more specialised. Like the case where a matrix might be upper triangular and in positive or non-negative definite form. Or where certain assumptions might be made about a matrix's eigenvalues.

There are some nice theorems proved about the spectral properties of various types of matrices. More to the point, the book has many useful ways to actually find the eigenvalues of such matrices. Where these methods might be more efficient than the generic methods of the earlier book.

A great reference source for advanced matrix analysis.......2000-08-28

Horn and Johnson's MATRIX ANALYSIS AND TOPICS IN MATRIX ANALYSIS are true classics (like Knuth's Art of Computer Programming). You will find classic theorems and lemmas in matrix theory and linear algebra here along with their proofs (some of these are not found elsewhere).

TOPICS IN MATRIX ANALYSIS contains a lot of stuff including LMI's, Kronecker and Hadamard products of matrices and their properties etc. I found this book indispensible when I was studying Semidefinite Programming.

Book Description

The book deals with the many connections between matrices, graphs, diagraphs and bipartite graphs. The basic theory of network flows is developed in order to obtain existence theorems for matrices with prescribed combinatorical properties and to obtain various matrix decomposition theorems. Other chapters cover the permanent of a matrix and Latin squares. The book ends by considering algebraic characterizations of combinatorical properties and the use of combinatorial arguments in proving classical algebraic theorems, including the Cayley-Hamilton Theorem and the Jorda Canonical Form.

Customer Reviews:

dense monograph.......2004-08-29

Sadly the authors have opted for a level
of abstraction that obscures many of the
beautiful details. Particularly disappointing
is the last chapter on matrix theory which veers
off into an odd mixture of marginalia which have
almost no applications.

An excellent treatise on applied combinatorics........1999-10-22

This book is an excellent resource for mathematicians, computer scientists, and engineers. The book shows how to use zero-one matrices and stochastic matrices in your work. The text pretty shows a lot of interesting properties different matrices have and how to compute various values associated with graphs from them. The book would be very useful for people interested in Neural Networks, Speech Recognition, Artificial Intelligence. It is mathematics, though and it describes the properties of the matrices and contains many proofs about these properties. Make sure that you have mastered linear algebra and combinatorics before reading this text.

Schaum's Outline of Theory and Problems of Matrix Operations

Average customer rating:

if you need a review
Quant helper
Excellent guide to matrix techniques
Delivers what is says on the box
Got matrix problems?

Schaum's Outline of Theory and Problems of Matrix Operations
Richard Bronson
Manufacturer: McGraw-Hill
ProductGroup: Book
Binding: Paperback

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ASIN: 0070079781

Book Description

If you want top grades and thorough understanding of matrix operations, this powerful study tool is the best tutor you can have! It takes you step-by-step through the subject and gives you 363 accompanying related problems with fully worked solutions. You also get plenty of practice problems to do on your own, working at your own speed. (Answers at the back show you how you're doing.) Famous for their clarity, wealth of illustrations and examples, and lack of dreary minutiae, Schaum’s Outlines have sold more than 30 million copies worldwide—and this guide will show you why!

Customer Reviews:

if you need a review.......2007-05-13

I got this book to try to make up for not haven taken linear algebra in school, because I am trying to learn to program in MatLab, whose name is derived from Matrix Labratory! So it works out, ie the book, to be a decent review for something I never actually studied!

Quant helper.......2007-02-13

Great book for review of linear algebra. I needed this book to check the results of code I had written for a quadratic beta routine.

Excellent guide to matrix techniques.......2005-12-03

Unlike the Schaum's outline of linear algebra, which is more about the physical interpretation of matrices as vectors, this Schaum's outline is good for learning techniques of solutions that were meant for large matrices. It is aimed at the applied mathematician, since there are not very many proofs as exercises. Instead, the user is taught the various algorithms used to solve matrix problems. The guide starts with very basic operations such as matrix addition, subtraction, and dot products. It then moves on to methods of solution for finding the determinant, eigenvalues and eigenvectors, and the functions of a matrix. What I particularly like about this guide is that in its more advanced section it shows in plain language how to implement singular value decomposition, the QR algorithm to compute eigenvalues, vector norms, LU decomposition, and other more advanced methods of solution that are not mentioned in basic linear algebra texts and are overloaded with theory in more advanced texts that lack practical examples. This book is an excellent companion to texts such as Trefethen and Bau's "Numerical Linear Algebra", since that book is short on worked examples and concentrates more on theory. The format of this guide is the same of most other Schaum's outlines- for each topic there are a few pages on motivation and the algorithms themselves, a section of worked problems, and a section of more problems with answers but not with complete solutions.

Delivers what is says on the box.......2005-08-29

Takes you right from the basics to complex stuff like QR decomposition and SVD. Very useful for programmers who want to gain knowledge on solving linear equations.

Got matrix problems?.......2002-08-27

If you do, this book is very helpful in that it gives a step-by-step approach to solving matrix operations problems. Although I wouldn't use this book by itself, I would recommend getting this to supplement the class. If you have already taken the class, then this is a good refresher or reference for you.

Book Description

This textbook is a new introduction to linear algebra for students who have completed the first year of calculus. In the spirit of modern instruction, this elementary presentation of the important ideas in linear algebra emphasizes conceptual understanding, developing applied examples, and working with realistic numerical data before introducing formal mathematical definition and operations. This text emphasizes geometric, symbolic, and numeric presentations of the subject. The first two chapters cover linear phenomena in both numeric and geometric settings. The symbolic manipulation of vectors and matrices is then introduced as a tool for the study of specific problems. Many examples, student exercises, and group project ideas are included.

Matrix Analysis for Statistics (Wiley Series in Probability and Statistics)

Average customer rating:

The principles of matrix algebra essential for advanced statistics
Use symbols in a confusing way

Matrix Analysis for Statistics (Wiley Series in Probability and Statistics)
James R. Schott
Manufacturer: Wiley-Interscience
ProductGroup: Book
Binding: Hardcover

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ASIN: 0471669830

Book Description

Matrix Analysis for Statistics, Second Edition provides in-depth, step-by-step coverage of the most common matrix methods now used in statistical applications, including eigenvalues and eigenvectors, the Moore-Penrose inverse, matrix differentiation, the distribution of quadratic forms, and more. The subject matter is presented in a theorem/proof format, allowing for a smooth transition from one topic to another. Proofs are easy to follow, and the author carefully justifies every step. Accessible even for readers with a cursory background in statistics, yet rigorous enough for students in statistics, this new edition is the ideal introduction to matrix analysis theory and practice.

Customer Reviews:

The principles of matrix algebra essential for advanced statistics.......2006-07-17

If queried, the mathematician that does not work in statistics will most likely not feel that there is a need for a separate course in matrices applied to statistics. There is no doubt that statisticians need to know a great deal about matrices, so the question comes down to whether the traditional math courses in linear algebra are sufficient. In either case, it is still of benefit to have one source that statisticians can consult as a reference for problems with matrices and this book can serve as that source.
Mathematicians with little experience in statistics will have no difficulty in understanding the contents of the book, as nearly all of it is mathematical rather than statistical in nature. The first three chapters are:

*) A review of elementary matrix algebra.
*) Vector spaces.
*) Eigenvalues and eigenvectors.

With the exception of ten pages devoted to random vectors in chapter 1, there were few major items gleaned from statistics. They could serve as the first three chapters of any book on matrix operations. While the remaining chapters do contain more statistical concepts, the overwhelming majority of the material does not involve problems in statistics. There are a large number of problems at the end of the chapters and solutions are not provided.
The remaining chapters are:

*) Matrix factorizations and matrix norms.
*) Generalized inverses.
*) Systems of linear equations.
*) Partitioned matrices.
*) Special matrices and matrix products.
*) Matrix derivatives and related topics.
*) Some special topics related to quadratic forms.

The level of difficulty is within the reach of an advanced undergraduate, although it was written for graduate students in statistics. In my opinion, previous experience in statistics would be helpful, but not required for a reader to understand the material. If you are looking for a book on matrix operations, this one will serve your purpose, independent of whether your focus is on statistics.

Published in Journal of Recreational Mathematics, reprinted with permission.

Use symbols in a confusing way.......2003-12-22

I can't recommend this book.

One problem is that the author uses symbol in a confusing way: declare without define, define without explaination, especially in the examples related to linear regression. It seems he just pick up symbols at random whenever he needs one in the middle of a proof, make an equation out of it. It's your role to figure out from the equation what this symbol is and why the author introduce this symbol.
More than that symbols are not used consistently. Z1, for example, is used to represent column vectors, row vectors, orthornormal vectors and centeralized observation vectors in very close sections without explanation. A vector just defined as a column vector can be multiplied with another column vector. Seems the author doesn't pay much attentions to such "small" aspects and this makes the book really hard to read.

Another problem is you won't know what the author is trying to do only after the whole algebraic series is finished.The objective is always the last to come. Won't it be nice to just add a few words before each a few steps to say what you are planning to do?

The last complaint is that there's not a simple geometric graph in this book. How can you imagine a book on the subject of both statistics and matrix don't have a illustrative graph on it?

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