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1. Matrix Algebra Useful for Statistics
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3. Quaternions and Rotation Sequences
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1. Matrix Algebra Useful for Statistics (Wiley Series in Probability and Statistics)
by Shayle R.Searle
list price: $120.00
our price: $120.00
(price subject to change: see help)
Asin: 0471866814
Catlog: Book (1982-08-19)
Publisher: Wiley-Interscience
Sales Rank: 531281
Average Customer Review: 5 out of 5 stars
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Book Description

An easy to understand guide to matrix algebra and its uses in statistical analysis. Presents material in an explanatory style instead of the formal theorem-proof format; the only background necessary is high school algebra. The self-contained text includes numerous applied illustrations, numerical examples, and exercises. ... Read more

Reviews (1)

5-0 out of 5 stars Definitively a classic
This is an excellent introductory book, although mostly oriented to people with a reasonably good mathematical background. Searle covers most, if not all, the matrix algebra that you may need to fully understand applications of mixed linear models. Chapters one to eight cover the essential operations (addition, multiplication, determinants, etc) as well as more advanced concepts (rank, canonical forms, inverse, etc). The rest of the book (chapters nine to fifteen) covers applications to statistics as well as advanced topics that can help you to understand how do some of the statistical packages work inside. The only mathematics book that I have read from cover to cover. Definitively a classic. ... Read more

2. Matrix Computations (Johns Hopkins Series in the Mathematical Sciences)
by Gene H. Golub, Charles F. Van Loan
list price: $45.95
our price: $39.52
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Asin: 0801854148
Catlog: Book (1996-11-01)
Publisher: Johns Hopkins University Press
Sales Rank: 22537
Average Customer Review: 4.23 out of 5 stars
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Reviews (13)

5-0 out of 5 stars One of the best books on the subject
This is the book I turn to first when I have to deal with a problem in numerical linear algebra, it's clearly written and has extensive references.

5-0 out of 5 stars THE CLASSIC reference for matrix computations!
This book is an invaluable reference for anyone working in matrix computations or linear algebra. I have been using it for years and found it to be clear and comprehensive

5-0 out of 5 stars Got Matrices?
This is one of the definitive texts on computational linear algebra, or more specifically, on matrix computations. The term "matrix computations" is actually the more apt name because the book focuses on computational issues involving matrices,the currency of linear algebra, rather than on linear algebra in the abstract. As an example of this distinction, the authors develop both "saxpy" (scalar "a" times vector "x" plus vector "y") based algorithms and "gaxpy" (generalized saxpy, where "a" is a matrix) based algorithms, which are organized to exploit very efficient low-level matrix computations. This is an important organizing concept that can lead to more efficient matrix algorithms.

For each important algorithm discussed, the authors provide a concise and rigorous mathematical development followed by crystal clear pseudo-code. The pseudo-code has a Pascal-like syntax, but with embedded Matlab abbreviations that make common low-level matrix operations extremely easy to express. The authors also use indentation rather than tedious BEGIN-END notation, another convention that makes the pseudo-code crisp and easy to understand. I have found it quite easy to code up various algorithms from the pseudo-code descriptions given in this book. The authors cover most of the traditional topics such as Gaussian elimination, matrix factorizations (LU, QR, and SVD), eigenvalue problems (symmetric and unsymmetric), iterative methods, Lanczos method, othogonalization and least squares (both constrained and unconstrained), as well as basic linear algebra and error analysis.

I've use this book extensively during the past ten years. It's an invaluable resource for teaching numerical analysis (which invariably includes matrix computations), and for virtually any research that involves computational linear algebra. If you've got matrices, chances are you will appreciate having this book around.

4-0 out of 5 stars from theory to practice.
A few years ago this book permitted me to go reliably from
theoretical linear algebra to practical large-scale numerical
computations, using also LAPACK. I think this is its place:
from the university course level to the practical side.
On the other hand, one cannot really say it is as readable
as, say, Numerical Recipes: it has a quite terse style.

3-0 out of 5 stars Still state of the art?
It is now 6 years ago when the last version of this once
superb book was released. Meanwhile, bunches of books
aiming a similiar audience were published. Some of them,
in particular G.W. Stewarts, are nowadays more seasonable.
Notably, the "iterative" sections ask for light
refreshments. The lack of references to appropriate
software routines in these parts is another disadvantage
which could be easily overcome in a new edition. ... Read more

3. Quaternions and Rotation Sequences : A Primer with Applications to Orbits, Aerospace and Virtual Reality
by J. B. Kuipers
list price: $35.00
our price: $29.05
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Asin: 0691102988
Catlog: Book (2002-08-19)
Publisher: Princeton University Press
Sales Rank: 92635
Average Customer Review: 4.72 out of 5 stars
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Book Description

Ever since the Irish mathematician William Rowan Hamilton introduced quaternions in the nineteenth century--a feat he celebrated by carving the founding equations into a stone bridge--mathematicians and engineers have been fascinated by these mathematical objects. Today, they are used in applications as various as describing the geometry of spacetime, guiding the Space Shuttle, and developing computer applications in virtual reality. In this book, J. B. Kuipers introduces quaternions for scientists and engineers who have not encountered them before and shows how they can be used in a variety of practical situations.

The book is primarily an exposition of the quaternion, a 4-tuple, and its primary application in a rotation operator. But Kuipers also presents the more conventional and familiar 3 x 3 (9-element) matrix rotation operator. These parallel presentations allow the reader to judge which approaches are preferable for specific applications. The volume is divided into three main parts. The opening chapters present introductory material and establish the book's terminology and notation. The next part presents the mathematical properties of quaternions, including quaternion algebra and geometry. It includes more advanced special topics in spherical trigonometry, along with an introduction to quaternion calculus and perturbation theory, required in many situations involving dynamics and kinematics. In the final section, Kuipers discusses state-of-the-art applications. He presents a six degree-of-freedom electromagnetic position and orientation transducer and concludes by discussing the computer graphics necessary for the development of applications in virtual reality. ... Read more

Reviews (18)

5-0 out of 5 stars An oustanding work on rotations for the practitioner
My graduate school work was in theoretical quantum mechanics, and was especially concentrated in the group properties of rotations. I can honestly say that I would have been twice as effective if I had this reference available then.

Kuiper does an outstanding job of pulling together the traditional matrix-based approach to describing rotations with the less-frequently encountered quaternion approach. In doing so, he clearly shows the benefits of the quaternion algebra, especially for computer systems modeling rigid body rotations and virtual worlds. The exposition is clear, concise, and aimed at the practitioner rather than the theoretician. The examples are taken from classical engineering problems -- a refreshing change from the quantum-mechanical problems I was used to from previous works on the subject.

Despite the practical foocus, though, there is plenty of material here for those more interested in understanding the minutia of the SO(3) symmetry group. And unlike most work in this field, he doesn't stop with algebra, but includes the calculus of rotation matrices and quaternions using material on kinematics and dynamics of rigid bodies, celestial mechanics, and rotating reference frames.

I give the book my highest recommendation. It should be considered an essential reference work for anyone who encounters rotational problems with any frequency.

--Tony Valle

4-0 out of 5 stars Good beginning, not enough for most applications
The book delivers exactly what it promises, an in-depth study of rotations using quaternions. However, if you are looking for a complete description of how to use quaternions, it is missing a lot.

Specifically it doesn't explain anything about interpolating rotations, which is absolutely required in the field of animation. After reading this book, I would recommend finding a copy of Ken Shoemake's article "Animating Rotation with Quaternion Curves", which explains slerp and squad, there are many references available on the Internet. The site has some code by Tim Sweeney (lead programmer for Unreal) under "Vector Math and Quaternions", which explains how to use quaternion logarithms to handles higher-order (Hermite, Bezier, TCB) interpolations. It could be argued that this is out of the scope of the book, but I suspect many people interested in buying this book will need this information. This is the main way quaternions are used in game programming, for example.

Still, this book gives you a good starting point and its explanation of Euler angles and conversion to/from is about the best I have ever read. The derivation of quaternions as an extension of complex numbers is quite easy to follow and has a very easy-going style, which still giving a firm mathematical basis.

5-0 out of 5 stars I am the Quaternion Book's Author
I merely want to share with you an excellent review of my Quaternion Book. The review appeared in the Nov/Dec'03 issue of Contemporary Physics, vol6., and was written by Dr Peter Rowlands, Waterloo University, UK. The review is herewith attached (if I may) otherwise I'll paste the text). It's probably too long --- but you now know where to find it. Here goes:

The following Book Review Appeared in Journal: Contemporary Physics},
Nov/Dec 2003,
vol 44, no. 6, pages 536 - 537 · · ·
Quaternions & Rotation Sequences
A Primer with Applications to Orbits, Aerospace, and Virtual Reality
Princeton University Press. 2002, £24.95(pbk), pp. xxii +
371, ISBN 0 691 10298 8.
Scope: Text.
Level: Postgraduate and Specialist. }

Quaternions are one of the simplest and most powerful
tools ever offered to the physicist or engineer. Unfortunately,
they are relatively little known because a centuryold
prejudice (the result of a family feud involving vector
theory) has been responsible for keeping them out of
university courses. The fact that quaternions have never
really found their true role has become a self-fulfilling
prophecy, despite their reappearance in various disguised
forms such as Pauli matrices, 4-vectors, and, in a complex
double form, in the Dirac gamma algebra. The straightforward
manipulation of this relatively simple formalism,
however, means that, to a quaternionist, such things as

Minkowski space-time and fermionic spin are no longer
mysterious unexplained physical concepts but merely
inevitable consequences of the fundamental algebraic
structure, while even ordinary vector algebra as David
Hestenes has shown (Space-Time Algebras, Gordon and
Breach, 1966) is much better understood in terms of its
quaternionic base. The immense value of the quaternion
algebra is that its products are ordinary algebraic products,
not the dot or cross products of standard vector algebra,
although they also include these concepts.

Despite many statements to the contrary, quaternions
are by no means short of serious applications, either. Often
in highly practical contexts, and, in every application that I
know of, where a quaternion formulation is possible, this
formulation is invariably superior to any more 'conventional'
alternative. Kuipers, in his splendid book, effectively
shows this in the eminently practical case of the aerospace

sequence and great circle navigation by demonstrating how
the same calculations are done, first by conventional matrix
methods, and then by quaternions. Rather than abstractly
defining quaternion algebra and then seeking possible
applications, he prepares the ground well by describing
the application first, and then developing the quaternion
methods which will solve it. It is not until chapter 5, in fact,
that quaternion algebra is seriously introduced. However,
Kuipers sets this on a
firm basis by establishing early on the connection with
complex numbers, matrices and rotations. These subjects
are discussed with great thoroughness in the early chapters.
The work is avowedly a primer, and so nothing is taken for
granted. The student can begin at the beginning and follow
the argument through stage by stage, with virtually no
prior knowledge of the subject. The real core of the
mathematical analysis comes in chapters 5 to 7, with solid
and relatively easy to follow treatments of quaternion
algebra and quaternion geometry, together with an algorithm
summary, relating quaternions to such things as
direction cosines, Euler angles and rotation operators. The
superiority of quaternion over, for example, matrix
methods is demonstrated by Kuipers' statement on p. 153
that the quaternion rotation operator (unlike the matrix
one) is 'singularity-free'. Following the main application to
the aerospace sequence and great circle navigation, there
are further chapters on spherical trigonometry, quaternion
calculus for kinematics and dynamics, and rotations in
phase space, with two final chapters devoted to applications
in electrical engineering (dipole radiation signals sent by a
source to a sensor, and then correlated using a processor)
and computer graphics.

The final application is especially interesting as quaternions
have been behind much of the rapid development of
computer graphics. One role that quaternions have always
fulfilled is their applicability to 3-dimensional structures,
and the otherwise difficult problem of rotation, especially
when time-sequencing is involved. Computer software
engineers have exploited this while physicists have missed
out. The creation of a 'natural' 3-dimensionality, using the
'vector' or imaginary part of quaternions was, of course,
the original reason for their creation; but, while the
remaining 'scalar' or real part was originally thought of
as a problem by the proponents of vector theory, it is now
seen as a bonus, allowing the incorporation of time as a
natural result of the algebra. We cannot escape the fact that
we live in time within a 3-dimensional spatial world, and
quaternion algebra appears to be the easiest way of
comprehending and manipulating this 3-or 4-dimension-
ality. Kuipers shows us examples of the exploitation of the
technique in aerodynamics, electrical engineering and
computer software design, but it also has relevance in
topology, quantum mechanics, and particle physics.

It is frankly as absurd for physicists and engineers to
neglect quaternions as it would be for them to disregard
complex numbers or the minus sign. It is important that
students get to learn about this spectacularly simple and
powerful technique as early as possible, and Kuipers has
provided us with the perfect opportunity of remedying a
massive defect in our technical education. His book has

everything that one could wish for in a primer. It is also
beautifully set out with an attractive layout, clear diagrams,
and wide margins with explanatory notes where appropriate.
It must be strongly recommended to all students of
physics, engineering or computer science.

(University of Liverpool)

4-0 out of 5 stars A good introduction to quaternions
Is it possible to recommend a book and still say that it needs revision? It needs revision precisely because it is a good book and may well find more readers. The book does what no other does as far as I know; it introduces quaternions in elementary terms and shows some, at least, of how useful the concept is. The topic is neglected in textbooks for students at this level and probably even more generally. And yet I do think that the author could revise this book substantially and produce a better one.

3-0 out of 5 stars A word of caution
I was very disappointed when I started reading the book and immediately noticed a number of errors in the formulae. These were most likely typos but still can be confusing at times. As the other reviewers mentioned, the book has a very interesting, and in my opinion very good, teaching sytle, but don't take all the formulae by heart if you are going to use it as a reference book.

(PS. My comments are on the first print of the book, I hope the errors have been corrected in the later prints.) ... Read more

4. Topics in Matrix Analysis
by Roger A. Horn, Charles R. Johnson
list price: $50.00
our price: $50.00
(price subject to change: see help)
Asin: 0521467136
Catlog: Book (1994-06-24)
Publisher: Cambridge University Press
Sales Rank: 323255
Average Customer Review: 5 out of 5 stars
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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.This should be welcomed by graduate students and researchers in a variety of mathematical fields and as an advanced text and modern reference book. ... Read more

Reviews (1)

5-0 out of 5 stars A great reference source for advanced matrix analysis
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.

Both these books are now available in paperback (cost around 30+) dollars each. I have recently purchased both copies and can only strongly recommend them to anyone else. ... Read more

5. Matrix Analysis
by Roger A. Horn, Charles R. Johnson
list price: $40.00
our price: $40.00
(price subject to change: see help)
Asin: 0521386322
Catlog: Book (1990-02-23)
Publisher: Cambridge University Press
Sales Rank: 226162
Average Customer Review: 4.2 out of 5 stars
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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. ... Read more

Reviews (5)

1-0 out of 5 stars Not for the uninitiated
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.

5-0 out of 5 stars An encyclopedic reference for matrix analysis and linear alg
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.

5-0 out of 5 stars Excellent book.... for the initiated
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.

Together with Golub and Van Loan's "Matrix Computations", this is THE linear algebra book to get, although only if you're sufficiently initiated.

5-0 out of 5 stars The most comprehensive and up-to-date reference/textbook.
If you need to know anything about matrices - this is the book. It cover all the basic theory. Perfect for graduate-level courses. The book also has lots of material relevant to optimization theory and can be used in Operations Research courses. One of the nice features is a comprehensive index that makes the book a perfect reference source. Nicely written and easy to read.

5-0 out of 5 stars Excellent treatment of the subject matter
Horn and Johnson are clear, interesting, and accurate. The book does a good job of both teaching and intriguing.USA ... Read more

6. Schaum's Outline of Matrix Operations
by RichardBronson
list price: $16.95
our price: $11.53
(price subject to change: see help)
Asin: 0070079781
Catlog: Book (1988-07-01)
Publisher: McGraw-Hill
Sales Rank: 125184
Average Customer Review: 4 out of 5 stars
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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! ... Read more

Reviews (2)

4-0 out of 5 stars Got matrix problems?
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.

The topics covered are inversions, determinants, vectors, eigenvalues and eigenvectors, functions, square matrices, hermitian and positive definite matrices, canonical bases, unitary transformations, and nonnegative and patterned matrices, among other topics. As with other books in the Schaum's series, there are supplementary questions to test your knowledge and understanding. Most of the answers are in the back.

4-0 out of 5 stars Clear, easy to understand tutorial on Matrices
This is a very nice book that covers a everything one needs to know about matrices, without the extra derivations and confusion associated with this math. Very nice examples are included in the book that show the use of matrices. ... Read more

7. Calculus by and for Young People (Ages 7, Yes 7 and Up)
by Donald Cohen
list price: $13.95
our price: $11.86
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Asin: 096216741X
Catlog: Book (1989-03-01)
Publisher: Don Cohen the Mathman
Sales Rank: 181998
Average Customer Review: 3.5 out of 5 stars
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Book Description

This book is a description of how young people, Don and some mathematicians, solved problems which involve infinite series, infinite sequences, functions, graphs, algebra, +, - important mathematical ideas. At the same time they do a lot of arithmetic, and use pineapples, the tower puzzle, with science to math activities, and the use of other hands-on materials. ... Read more

Reviews (2)

5-0 out of 5 stars Calculus isn't beyond the reach of the average kid!
This is an outstanding book because it takes the mumbo-jumbo out of traditionally taught calculus and makes the ideas accessible to ANYONE, not just to math whizzes. The technical vocabulary and symbolic notation can always be learned later. This book introduces the important ideas of calculus with simple, natural language and, most helpful of all, illuminating graphics, so the beauty (yes, beauty) and fun of calculus comes through. I would recommend this book to anyone who is teaching children, and also to math phobics. (I am the former, and was the latter for many years.) This book is FUN, and it makes calculus FUN!

2-0 out of 5 stars This book is too small for the price
Before you buy this book be aware that it measures [approximately] less than 3x5". However, Donald Cohen has some great ideas. It is true that you can easily introduce younger students to the type of thinking that will be necessary in precalculus and up. I think it is worth it to get the workbook, which covers most of the material presented in this book. But don't buy both. ... Read more

8. Matrix Population Models: Construction, Analysis, and Interpretation
by Hal Caswell
list price: $77.95
our price: $77.95
(price subject to change: see help)
Asin: 0878930965
Catlog: Book (2000-09-01)
Publisher: Sinauer Associates
Sales Rank: 260280
Average Customer Review: 5 out of 5 stars
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Book Description

Matrix Population Models, Second Edition, is a comprehensive treatment of matrix population models and their applications in ecology and demography. It begins with simple cases, presented in detail so that beginning students can learn how to use these powerful models. It goes on to cover advanced topics in stochastic and nonlinear models. Analytical methods and theoretical issues are illustrated with empirical examples throughout.

The decade since the publication of the First Edition of this book has seen enormous progress in the theory and application of matrix population models. The new edition includes greatly expanded treatment of stochastic and density-dependent models, sensitivity analysis, and statistical inference, and new chapters on parameter estimation, structured population models, demographic stochasticity, and applications of matrix models in conservation biology.

Matrix Population Models, Second Edition, is an indispensable reference for graduate students and researchers in ecology, population biology, conservation biology, and human demography. ... Read more

Reviews (2)

5-0 out of 5 stars a classic - worth the wait
As a graduate student many years ago, I bought the last shelf copy of the first edition to Caswell's text on matrix population models for our bookstore. After 10+ years of using the book, both in research, and teaching, I'm glad I did. The 2nd edition is a lucid and masterful update, with several nice touches that should be appreciated by both newcomers and experienced modelers. In particular, some of the more turgid text from the first edition has been clarified, and expanded, and several new very important chapters have been added (yes, using branching process theory you can handle demographic stochasticity with matrix models). A superb book, made even better by the inclusion (at last!) of some basic MATLAB code for some of the more esoteric calculations. My only complaint (related perhaps to the 'code') is that the many good 'worked examples' are not treated more fully. I'd have liked to have seen the actual matrices involved, or some further detail, in some cases, rather than a figure or table summarizing the results. However, a minor complaint - perhaps easily solved by a companion website with code for each example in the book 9something I'm probably going to do on my own, but should be standard these days for any technical text).

5-0 out of 5 stars Clear and accessible introduction to population modeling
There is often a false dichotomy drawn between differential (or difference) equation models of populations and agent-based (artificial life, individual-based, configuration) models. Agent-based models can represent more of the complexity of biological systems at the expense of analytical tractability. Matrix population models form a bridge between the two approaches.

Caswell shows how you can elaborate differential equation models to represent much of the population structure and characteristics of interest within a population. His descriptions are clear and easily accessible to biologists as well as people from the more quantitative fields of science.

The new edition of this book is due out in April 2000. I am looking forward to it. ... Read more

9. Matrix Differential Calculus with Applications in Statistics and Econometrics, 2nd Edition
by Jan R.Magnus, HeinzNeudecker
list price: $95.54
our price: $95.54
(price subject to change: see help)
Asin: 047198633X
Catlog: Book (1999-03-15)
Publisher: John Wiley & Sons
Sales Rank: 461794
Average Customer Review: 4.6 out of 5 stars
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Book Description

Matrix Differential Calculus With Applications in Statistics and Econometrics Revised Edition Jan R. Magnus, CentER, Tilburg University, The Netherlands and Heinz Neudecker, Cesaro, Schagen, The Netherlands " .deals rigorously with many of the problems that have bedevilled the subject up to the present time." - Stephen Pollock, Econometric Theory "I continued to be pleasantly surprised by the variety and usefulness of its contents " - Isabella Verdinelli, Journal of the American Statistical Association Continuing the success of their first edition, Magnus and Neudecker present an exhaustive and self-contained revised text on matrix theory and matrix differential calculus. Matrix calculus has become an essential tool for quantitative methods in a large number of applications, ranging from social and behavioural sciences to econometrics. While the structure and successful elements of the first edition remain, this revised and updated edition contains many new examples and exercises.
* Contains the essentials of multivariable calculus with an emphasis on the use of differentials
* Many new examples and exercises
* Fulfils the need for a unified and self-contained treatment of matrix differential calculus
* Includes new developments in this field
Part I presents a concise, yet thorough overview of matrix algebra, while the second part develops the theory of differentials. The remaining Parts III to VI combine the theory and application of matrix differential calculus providing the practitioner and researcher with both a quick review and a detailed reference. Visit our web page
... Read more

Reviews (5)

4-0 out of 5 stars Bad typesetting reviews are not exaggerating
I have read the bad reviews regarding the typesetting of this book and I thought they were exaggerating. Nevertheless, I have borrowed this book (old edition/hardcover) from the University library and I thought that buying it was worthwile.When I ordered the book I found out that the book quality was even worse than expected. The typesetting is worse than a photocopied book; I even thought that this was not an authentic copy but a cheap one from a Banana country. Nevertheless, when you open to read the book pages are coming out. The hardcover edition price -$300$- is ridiculous. I am a postoctoral fellow in engineering and I cannot afford more than $100 for a book. The $80 dollar price is not justified for that bad typesetting. This is a very helpful book for a graduate engineering student but I doubt that I will recommend it for buying. I will have to think seriously about buying another book from Wiley piblishers.

5-0 out of 5 stars Too bad!
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!

5-0 out of 5 stars Very useful book, bad typesetting
the authors provided a really nice treatment on the not-so-popular subject. The presentation is clear and readable. I just want to second the review below : the typesetting quality is inferior to a photocopied book ( or one may feel it's like a book published in 70's)

5-0 out of 5 stars enormous utility
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.

4-0 out of 5 stars Excellent, no-nonsense compilation of results
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. ... Read more

10. Fundamentals of Matrix Computations
by David S.Watkins
list price: $105.00
our price: $105.00
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Asin: 0471213942
Catlog: Book (2002-05-15)
Publisher: Wiley-Interscience
Sales Rank: 340492
Average Customer Review: 4.5 out of 5 stars
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Book Description

A significantly revised and improved introduction to a critical aspect of scientific computation
Matrix computations lie at the heart of most scientific computational tasks. For any scientist or engineer doing large-scale simulations, an understanding of the topic is essential. Fundamentals of Matrix Computations, Second Edition explains matrix computations and the accompanying theory clearly and in detail, along with useful insights.
This Second Edition of a popular text has now been revised and improved to appeal to the needs of practicing scientists and graduate and advanced undergraduate students. New to this edition is the use of MATLAB for many of the exercises and examples, although the Fortran exercises in the First Edition have been kept for those who want to use them. This new edition includes:
* Numerous examples and exercises on applications including electrical circuits, elasticity (mass-spring systems), and simple partial differential equations
* Early introduction of the singular value decomposition
* A new chapter on iterative methods, including the powerful preconditioned conjugate-gradient method for solving symmetric, positive definite systems
* An introduction to new methods for solving large, sparse eigenvalue problems including the popular implicitly-restarted Arnoldi and Jacobi-Davidson methods
With in-depth discussions of such other topics as modern componentwise error analysis, reorthogonalization, and rank-one updates of the QR decomposition, Fundamentals of Matrix Computations, Second Edition will prove to be a versatile companion to novice and practicing mathematicians who seek mastery of matrix computation.
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Reviews (2)

4-0 out of 5 stars good, but not the best
when i first saw this book, i was very excited. i would have rated it 5 stars at that time. It's a much easier read than Golub's "matrix computations" and Demmel's "Applied Numerical Linear Algebra".

but then I saw Trefethen and Bau's "Numerical Linear Algebra", and I was totally amazed by that book. By comparison, this book by Watkins can only be rated 4 stars. It just doesn't match up to Trefethen's book in terms of elegance, smoothness, intuitiveness, and more importantly, focusing on the essence instead of being buried in the details.

if you are really interested in the topic of matrix computation, I suggest you start with Trefethen's book, and use Golub's book as reference later on.

5-0 out of 5 stars interesting alternative to golub/van loan
This book is not that famous as the golub/van loan bible but it is more than competitive. Especially for undergraduate or even graduate students who want to become familiar with computational aspects of linear algebra the bible might be to compact; watkins gives one more help to understand the main ideas. ... Read more

11. Matrices and Linear Algebra (Dover Books on Advanced Mathematics)
by Hans Schneider, George Phillip Barker
list price: $16.95
our price: $11.53
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Asin: 0486660141
Catlog: Book (1989-06-01)
Publisher: Dover Publications
Sales Rank: 81963
Average Customer Review: 5 out of 5 stars
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Book Description

Basic textbook covers theory of matrices and its applications to systems of linear equations and related topics such as determinants, eigenvalues and differential equations. Numerous exercises, both true-false and multiple choice, with each chapter. Answer section.
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Reviews (1)

5-0 out of 5 stars Clearly exposed an important math field
This book is very useful not only as an introduction to the college math but also as an alternative high school book. One of the best investion I have ever made! Get it - now. ... Read more

12. Matrix Analysis (Graduate Texts in Mathematics, 169)
by Rajendra Bhatia
list price: $59.95
our price: $51.56
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Asin: 0387948465
Catlog: Book (1996-12-01)
Publisher: Springer-Verlag
Sales Rank: 92870
Average Customer Review: 5 out of 5 stars
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Book Description

The aim of this book is to present a substantial part of matrix analysis that is functional analytic in spirit. Much of this will be of interest to graduate students and research workers in operator theory, operator algebras, mathematical physics and numerical analysis. The book can be used as a basic text for graduate courses on advanced linear algebra and matrix analysis. It can also be used as supplementary text for courses in operator theory and numerical analysis. Among topics covered are the theory of majorization, variational principles for eigenvalues, operator monotone and convex functions, perturbation of matrix functions and matrix inequalities. Much of this is presented for the first time in a unified way in a textbook. The reader will learn several powerful methods and techniques of wide applicability, and see connections with other areas of mathematics. A large selection of matrix inequalities will make this book a valuable reference for students and researchers who are working in numerical analysis, mathematical physics and operator theory. ... Read more

Reviews (1)

5-0 out of 5 stars An excellent book on this topic!
This book is an expansion of the author's lecture notes "Perturbation Bounds for Matrix Eigenvalues" published in 1987. I have used both versions for my students' projects. The book under review centers around the themes on matrix inequalities and perturbation of eigenvalues and eigenspaces. The first half of the book covers the "classical" material of majorisation and matrix inequalities in a very clear and readable manner. The second half is a survey of the modern treatment of perturbation of matrix eigenvalues and eigenspaces. It includes lots of recent research results by the author and others within the last ten years. This book has a large collection of challenging exercises. It is an excellent text for a senior undergraduate or graduate course on matrix analysis. ... Read more

13. Iterative Solution of Large Sparse Systems of Equations (Applied Mathematical Sciences)
by Wolfgang Hackbusch
list price: $84.95
our price: $84.95
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Asin: 0387940642
Catlog: Book (1994-01-01)
Publisher: Springer-Verlag
Sales Rank: 944821
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Book Description

This book presents the description of the state of modern iterative techniques together with systematic analysis. The first chapters discuss the classical methods. Comprehensive chapters are devoted to semi-iterative techniques (Chebyshev methods), transformations, incomplete decompositions, gradient and conjugate gradient methods, multi-grid methods and domain decomposition techniques (including e.g. the additive and multiplicative Schwartz method). In contrast to other books all techniques are described algebraically. For instance, for the domain decomposition method this is a new but helpful approach. Every technique described is illustrated by a Pascal program applicable to a class of model problem. ... Read more

14. Elementary Matrix Algebra (Dover Books on Mathematics)
by Franz Edward Hohn, Franz E. Hohn
list price: $24.95
our price: $16.97
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Asin: 0486425347
Catlog: Book (2003-01-01)
Publisher: Dover Publications
Sales Rank: 288115
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Book Description

This complete and coherent exposition, complemented by numerous illustrative examples, offers readers a text that can teach by itself. Fully rigorous in its treatment, it offers a mathematically sound sequencing of topics, starting with the most basic laws of matrix algebra and progressing to the sweepout process for obtaining the complete solution of any given system of linear equations, homogeneous or nonhomogeneous, and the role of matrix algebra in the presentation of useful geometric ideas, techniques, and terminology. Other subjects include the complete treatment of the structure of the solution space of a system of linear equations; the most commonly used properties of determinants, and linear operators and linear transformations of coordinates. 1973 ed.
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15. Lie Groups, Lie Algebras, and Representations
by Brian C. Hall
list price: $59.95
our price: $51.56
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Asin: 0387401229
Catlog: Book (2003-08-07)
Publisher: Springer-Verlag
Sales Rank: 130371
Average Customer Review: 5 out of 5 stars
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Book Description

This book addresses Lie groups, Lie algebras, and representation theory. In order to keep the prerequisites to a minimum, the author restricts attention to matrix Lie groups and Lie algebras. This approach keeps the discussion concrete, allows the reader to get to the heart of the subject quickly, and covers all of the most interesting examples. The book also introduces the often-intimidating machinery of roots and the Weyl group in a gradual way, using examples and representation theory as motivation.

The text is divided into two parts. The first covers Lie groups and Lie algebras and the relationship between them, along with basic representation theory. The second part covers the theory of semisimple Lie groups and Lie algebras, beginning with a detailed analysis of the representations of SU(3). The author illustrates the general theory with numerous images pertaining to Lie algebras of rank two and rank three, including images of root systems, lattices of dominant integral weights, and weight diagrams. This book is sure to become a standard textbook for graduate students in mathematics and physics with little or no prior exposure to Lie theory.

Brian Hall is an Associate Professor of Mathematics at the University of Notre Dame. ... Read more

Reviews (2)

5-0 out of 5 stars A refreshingly clear introductory text on Lie groups
I rarely have time or feel strongly enough about a text to write a review. However, with Hall's book, I feel compelled. After struggling with the rather compact sixth chapter of Wulf Rossman's book on representations of Lie groups and algebras during a course on representation theory (the first five chapters were assumed), I turned to this one, and boy, am I ever glad I did.

The main and overriding strength of this book is the willingness of the author to guide the reader in digesting definitions and proofs. This comes in the form of numerous examples and counterexamples to point the reader in the right direction after a definition. And Hall constantly reminds readers of particular relevant terms in the course of applying them, which I found very effective in reinforcing concepts, and which allowed me to focus on the task at hand rather than spending time sifting through previous chapters, often losing sight of the main point of the argument.

Another strong point is the approach taken to introducing weights and roots of particular representations. I have found this a very difficult subject (as I guess a lot of students do) and Rossman's book was not helping much. As the previous reviewer noted, this book starts out (chapters four and five) with detailed treatments of the representations of su(2) and su(3) via the complexifications sl(2; C) and sl(3; C) and introduces weights in these contexts as pairs of simultaneous eigenvalues of the basis elements of the Cartan subalgebra.This requires only a background in linear algebra to digest and really hits home the point of these constructs in the whole scheme of things. After these examples under the belt, the reader is then able to take in the general definition of a weight as a linear functional in chapter six. Representations of general semisimple Lie algebras are covered in chapter seven.

Throughout it all, Hall's style is very clear and his proofs are complete and illuminating. If you have had courses in linear and modern algebra, you should be fine with this one. Very well suited for self study. I can't recommend this book highly enough.

This book focuses on matrix Lie groups and Lie algebras, and their relations and representations. This makes things a bit simpler, and not much is lost, because most of the interesting Lie groups & algebras are (isomorphic to)groups & algebras of matrices.
I believe that most mathematicians are more concerned with impressing their colleagues with their subtlety and erudition than they are in making a clear, simple and comprehensible presentation. This is mitigated by the publisher's insistence that the first 10 pages be clear to a mid-level undergraduate so the book will sell. So I usually get stuck at page 10 in those books.
This book is clear (to me) at least to page 168 (as far as I have progressed). There are even appendices on finite groups and key aspects of linear algebra. After introducing the classical groups and their algebras and the exponential map relating one to the other, the author introduces representations. He then details the representations of sl(2,C) and sl(3,C) (a.k.a. the complexifications of su(2) and su(3), respectively). By going through the details on these [with their Cartan subalgebras, weights, roots, Weyl groups, etc.], the general theory that follows is more palatable than it might otherwise be. Little rigor is sacrificed (if I am qualified to judge that - probably not). A few proofs are left out, but not many.

Another virtue of this book is that there are very few mistakes. I have trouble distinguishing an author's typos from my thinkos, so this is a particularly impotant feature of this book.
I very highly recoommend this book to anyone who does not already know the subject; it would be a perfect first book on this area. This book is really written with the student in mind. As a "shade - tree" mathematician, I need all the help I can get in understanding this difficult subject. Hall has done the best job I have seen at making the theory accessible without sacrificing rigor. ... Read more

16. Matrix Algebra : An Introduction (Quantitative Applications in the Social Sciences)
by Krishnan Namboodiri
list price: $15.95
our price: $15.95
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Asin: 0803920520
Catlog: Book (1984-07-01)
Publisher: SAGE Publications
Sales Rank: 111432
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Book Description

Defines basic terms and elementary matrices manipulation, introduces the concept of linear dependence, and explains eigenvalues and eigenvectors with illustrated examples.

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17. Basic Matrix Algebra with Algorithms and Applications
by Robert Liebler
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Asin: 1584883332
Catlog: Book (2002-12-13)
Publisher: Chapman & Hall/CRC
Sales Rank: 967976
Average Customer Review: 4 out of 5 stars
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Book Description

Clear prose, tight organization, and a wealth of examples and computational techniques make Basic Matrix Algebra with Algorithms and Applications an outstanding introduction to linear algebra. The author designed this treatment specifically for freshman majors in mathematical subjects and upper-level students in natural resources, the social sciences, business, or any discipline that eventually requires an understanding of linear models. With extreme pedagogical clarity that avoids abstraction wherever possible, the author emphasizes minimal polynomials and their computation using a Krylov algorithm. The presentation is highly visual and relies heavily on work with a graphing calculator to allow readers to focus on concepts and techniques rather than on tedious arithmetic. Supporting materials, including test preparation Maple worksheets, are available for download from the Internet.This unassuming but insightful and remarkably original treatment is organized into bite-sized, clearly stated objectives. It goes well beyond the LACSG recommendations for a first course while still implementing their philosophy and core material. Classroom tested with great success, it prepares readers well for the more advanced studies their fields ultimately will require. ... Read more

Reviews (1)

4-0 out of 5 stars Good Book, Great Sense of Humor .
Good, but COULD be better . . I think the book, having few typos, lacks in concrete explanations ( although quite some are there ) and instead, beats a bit with words around the bush, etc . I interpret some sections of chapters in full clarity entirely, yet still get lots vaguely . Very clear objectives and nice examples with great practice problems; I would recommend more geometrical interpretative topics to aid with a visual relationship of some topics . Overall good . ... Read more

18. Matrix Algebra From a Statistician's Perspective
by David A. Harville
list price: $89.95
our price: $89.95
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Asin: 038794978X
Catlog: Book (1997-09-05)
Publisher: Springer-Verlag
Sales Rank: 405438
Average Customer Review: 4.67 out of 5 stars
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Book Description

This book presents matrix algebra in a way that is well-suited for those with an interest in statistics or a related discipline. 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. It includes a number of very useful results that have heretofore only been available from relatively obscure sources. Detailed proofs are provided for all results. Due to its wealth of results, this should be a must-have text for anyone in need of a reference on matrix algebra.

David A.Harville is a research staff memeber in the Mathematical Sciences Department of the IBM T.J.Watson Research Center. Prior to joining the Research Center he spent ten years as a mathematical statistician in the Applied Mathematics Research Laboratory of the Aerospace Research Laboratories (at Wright-Patterson,AFB, Ohio,followed by twenty years as a full professor in the Department of Statistics at Iowa State University. He has extensive experience in the area of linear statistical models, having taught (on numberous occasions) M.S.and Ph.D.level courses on that topic,having been the thesis adviser of 10 Ph.D. students,and having authored over 60 research articles. His work has been recognized by his election as a Fellow of the American Statistical Association and the Institute of Mathematical Statistics and as a memeber of the International Statistical Institute and by his having served as an associate editor of Biometrics and of the Journal of the American Statistical Association.

The style and level of presentation are designed to make the contents accessible to a broad audience. The book is essentially self-contained, though it is best-suited for a reader who has had some previous exposure to matrices (of the kind that might be acquired in a beginning course on linear or matrix algebra). It will be a valuable reference for statisticians and for others. As it includes exercise sets, it can serve as the primary text for a course on matrices or as a supplementary text in courses on such topics as linear statistical models or multivariate analysis. ... Read more

Reviews (3)

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. (2) author can use more clear or simple way to describe many basic concepts but he does not do it! (if you have taken Linear Algebra from math, you will understand what I mean). Overall, this is a pretty good bookfor beginners.

5-0 out of 5 stars Execllent reference, even for non-statisticians
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.

5-0 out of 5 stars An excellent book on matrices
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. ... Read more

19. Matrix Algebra: Exercises and Solutions
by David A. Harville
list price: $44.95
our price: $44.95
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Asin: 0387953183
Catlog: Book (2001-09-06)
Publisher: Springer-Verlag
Sales Rank: 680986
Average Customer Review: 2 out of 5 stars
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Book Description

This book contains over 300 exercises and solutions covering a wide variety of topics in matrix algebra. They can be used for independent study or in creating a challenging and stimulating environment that encourages active engagement in the learning process. Thus, the book can be of value to both teachers and students. The requisite background is some previous exposure to matrix algebra of the kind obtained in a first course. The exercises are those from an earlier book by the same author entitled Matrix Algebra From a Statistician's Perspective (ISBN 0-387-94978-X). They have been restated (as necessary) to stand alone, and the book includes extensive and detailed summaries of all relevant terminology and notation. The coverage includes topics of special interest and relevance in statistics and related disciplines, as well as standard topics. ... Read more

Reviews (1)

2-0 out of 5 stars too dry
The book consists of a seemingly endless number
of exercises whose solutions give little or
no insight into the structure underlying the
problems. The final result is that you are no
smarter at the end than at the beginning. ... Read more

20. Combinatorial Matrix Theory (Encyclopedia of Mathematics and its Applications)
by Richard A. Brualdi, Herbert J. Ryser
list price: $120.00
our price: $120.00
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Asin: 0521322650
Catlog: Book (1991-07-26)
Publisher: Cambridge University Press
Sales Rank: 410320
Average Customer Review: 4 out of 5 stars
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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. ... Read more

Reviews (1)

4-0 out of 5 stars An excellent treatise on applied combinatorics.
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. ... Read more

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