Product 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. ... Read more

Customer Reviews (7)

Good content with bad presentation
I purchased it to prepare myself in order to take a PhD selection exam in Economics. The content is superb, unfortunately the type isn't good.

essential guide to matrix calculus
I am unusually lucky to get around the typesetting problems described by other reviewers: I was translating the book into Russian a few years ago based on the authors' LaTeX files, so I am not even sure I saw the Wiley book printed. I also was able to receive the author copy from the Russian publisher for free. Of course Wiley's price of $300 is ridiculous! The authors complained about it, too, seeing this as an objective obstacle for dissemination, but there is little they could do about the price.

I have not appreciated the book that much until I hit the need for matrix calculus for my dissertation research. Knowing the book fairly closely, I was able to find the results I needed in 15 minutes, and applying them to my problem provided a huge leap in the generality of results, as well as shortened the derivations from about 15 pages of ugly element by element computations to about three pages. Two thumbs up!

The book also contains a wealth of important mathematical results and makes the reader think rigorously about their notation (which is important for both matrix computations and for caclulus, thus making it at least twice as important in matrix calculus), so it can be targeted not only at statistical and econometric audiences, but can also serve as a useful supplement to a linear algebra course.

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 pagesare coming out. The hardcover edition price -$300$- is ridiculous. I am a postoctoral fellow in engineeringand 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 anotherbook from Wiley piblishers.

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!

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) ... Read more

Product Description
The masterminds behind The Matrix, The Matrix Reloaded and The Matrix Revolutions unveil a second collection of comics tales based on their epic creation, starring some of the biggest names in comics! Spinning out of concepts by the Wachowski Brothers, this new volume features stories and artwork by, amongst others, Geof Darrow (conceptual designer on all three films, co-creator of Hard Boiled), Steve Skroce (storyboard artist on the films), Bill Sienkiewicz (Elektra: Assassin) and Tim Sale (Batman: The Long Halloween). Exploring every facet of the Matrix universe and expanding upon the mythos of the movies, The Matrix Comics 2 is essential reading for any fan. ... Read more

Product Description
World-renowned Buddhist scholar Herbert V. Guenther here offers the first comprehensive study of the rDzogs-chen or Ati tradition of the Nyingma school of Tibetan Buddhism.Matrix of Mystery explores man's ability to preserve as well as transmit essential insights into the structure of reality.

Utilizing a key root Buddhist scripture, theGuhyagarbha ("Matrix of Mystery"), along with dozens of commentarial Tibetan textual sources, Guenther presents the most profound teachings of the Buddhist tradition, which represent the culmination of religious thought and practice in Tibet. In relating these teachings in modern scientific and humanistic perspectives, he demonstrates how, in many cases, the traditional religious and modern secular perspectives on the nature of reality interface.

Professor Guenther discusses the mandala and the deities that reside therein; the organizing principles of body, speech, mind, quality, and action, the three bodies of the buddha (trikaya); the inseparability of prajna and skillful means; and the complex field of Buddhist iconography. Throughout, quotations from numerous Tibetan sources are used to illustrate various teachings. His book will appeal to any serious student of Tibetan Buddhism. ... Read more

Customer Reviews (4)

Don't torture yourself
Most Buddhist authors write from a pure intention. No doubt they realise it's quite likely they will return to this planet in their next life - and they'd like to do something to improve it.

Dr Güenther was clearly an exception, if his books are anything to go by.

Matrix of Mystery ("mystery" being the operative word) is yet another demonstration that he was a (clearly compassionless) tree-wasting show-off windbag, more interested in demonstrating his great erudition than sharing any insight he MAY have had.

I challenge anyone on this planet to explain to us what he was going on about - and I include in that challenge all the high lamas of this earth. The reason his writings are incoherent is not necessarily because they are profound (who would know?!) but because he didn't put in the effort to make them CLEAR to readers. If he had any realisation at all, he didn't share it.

He wasted his life.

(Moreover, it seems like he had close access to some important teachers. So he also wasted what they gave him. This is not good, because that time, space, and energy could have been used by someone else who might have actually done something USEFUL with it.)

If karma is any guide, who knows what realm of confusion he now inhabits?

***

PS To other reviewers who give good reviews to wasted paper like this, I can only say: just because everyone else is dancing to the trendy new song, doesn't mean you have to rush out on the dance floor. Just because you might look like a fool if you don't understand something, doesn't mean the person saying it does either.

With all the confusion and misinformation that clearly reigns in the world right now, what we need is CLARITY. And it is the least we can expect from those who 'know better' - who have ANY realisation. It's their duty to share it, not use it to aggrandise themselves.

Yes, the intellect itself is also one of the six senses, something for us to enjoy. But when the house is burning down around your family and you have access to water, you don't use it to write a thesis about microscopic phenomena to impress all your academic friends. You pick up a large bucket of it and you throw it on the fire! :-)

Mystery indeed
This book should be undertaken as a study--it is not a light read.

Too difficult to understand for me, sorry. Nothing practical in it, only theory.

The Risks and Rewards of Syncretic Utterance...
Walter Benjamin imagined himself writing a book wholly of quotations from other writers.(_The Arcades Project_ represents one way he moved in that direction as a writer.)Herbert Guenther has developed not a pastiche literary work but a pastiche language in which he translates and interprets the Dzogchen message, lifting terms from phenomenology (esp. Heidegger and Merleau-Ponty), quantum mechanics (esp. David Bohm), and 1970's cognitive science and computer jive.I don't know if this appraoch successfully transmits Dzogchen praxis (I'm no guru, friends), but it's clear to me that this book is precious on its own terms.

Really, it's an interesting performance.This is not your conventional "Dharma book."It's not meant to make you comfortable or to reassure you about anything.Guenther's specific dialect of syncretese is not easy on the first reading, but the specialized vocabulary (meaning-saturated gestalt vs. scenario gestalt vs. display gestalt) leads to a very precise presentation, if one is willing to really try to follow what Guenther is trying to do with the ideas he's constructed.You just have to dig in and work at it if you're going to enjoy your time with this book.

I think this book is cool, to be straight with you.It's cool in the same way that Montreal's ambitious and excessive Olympic Stadium is cool, or Arcosanti, or Deleuze and Guattari's _Capitalism and Schizophrenia_.Like all these, _Matrix of Mystery_ arose in that bold zeitgeist of world-excavation, world-creation, and earnest experimentation.That the surfaces and contours are unfamiliar and largely uninviting to those used to Wal-Mart/McDo's architecture is not indicative of any flaws in those shapes and smoothnesses, and is basically tough bananas.There's always NASCAR.

_Matrix of Mystery_ is beautiful.

And like Olympic Stadium or Deleuze and Guattari (or postmodern anything), not everyone is ready to give it an earnest and openminded look.There are many paths for many people.Even those ridiculous Disney Channel movies are a part of the knowledge business, if your attitude is right.

Intrigued?Give it a shot.In any event, may you find your path.

the best accounting of the human condition available now
This is more than a book.It is a study.I have been studying it for almost 15 years.Well worth the time and effort.

Get out your dictionary.Msrs G and Longchenpa are very exact.They say more in aparagraph than most "experts" on the human mind and livingnesssay in a lifetime.

Mr G and L deserve highest praise.

Michael Mourer ... Read more

Product Description
A phantom haunts America-the ghost of Dealey Plaza where President John F. Kennedy was shot on November 22, 1963. In Matrix for Assassination, author Richard Gilbride, a schoolboy in 1963 who became fascinated with the facts, condenses much of the research conducted in recent years after a mountain of new data became available from classified files with the passing of the John F. Kennedy Assassination Records Collection Act of 1992.

Matrix for Assassination names the names. It offers simple and defensible solutions to many of the crime's lasting enigmas:

• Who were the shooters?
• Who forced Ruby to kill Oswald?
• Who orchestrated Kennedy's autopsy cover-up?
• What actually happened in the book depository?
• Were the Dallas police in on the plot? The Pentagon? LBJ? The CIA?

Customer Reviews (2)

Interesting book on the JFK assassination
As the leading civilian authority on the United States Secret Service, I was thrilled to be referenced several times in this interesting volume on the JFK assassination. Mr. Gilbride is to be commended for writing a well put together volume. While I don't agree with all of his work, this is a good addition to the library. Buy it!

Eclectic, But Worthwhile
Author explores a variety of tangents, some too far out for my taste. Worthwhile alone for the initial publication of a blockbuster McCone to Rowley file which concedes ONI/CIA status of LHO. Good look at Second Oswald, Ruby/Mob connections, Warren Commission weaknesses, etc. Even for the serious researcher, there is considerable fresh data and analysis. Recommended. ... Read more

Product Description

From the Foreword, written by legendary nano pioneer M. Meyyappan, Chief Scientist for Exploration Technology NASA Ames Research Center, Moffett Field, California, USA:

"…there is critical need for a book to summarize the status of the field but more importantly to lay out the principles behind the technology. This is what Professor Arvind Agarwal and his co-workers … have done here."

Carbon Nanotubes: Reinforced Metal Matrix Composites reflects the authors’ desire to share the benefits of nanotechnology with the masses by developing metal matrix carbon nanotube (MM-CNT) composites for large-scale applications. Multiwall carbon nanotubes can now be produced on a large scale and at a significantly reduced cost. The book explores potential applications and applies the author’s own research to highlight critical developmental issues for different MM-CNT composites—and then outline novel solutions.

With this problem-solving approach, the book explores:

• Advantages, limitations, and the evolution of processing techniques used for MM-CNT composites
• Characterization techniques unique to the study of MM-CNT composites—and the limitations of these methods
• Existing research on different MM-CNT composites, presented in useful tables that include composition, processing method, quality of CNT dispersion, and properties
• The micro-mechanical strengthening that results from adding CNT
• The applicability of micro-mechanics models in MM-CNT composites
• Significance of chemical stability for carbon nanotubes in the metal matrix as a function of processing, and its impact on CNT/metal interface and mechanical properties
• Computational studies that have not been sufficiently covered although they are essential to research and development
• The critical issue of CNT dispersion in the metal matrix, as well as a unique way to quantify CNT distribution and subsequently improve control of the processing parameters for obtaining improved properties

Carbon Nanotubes: Reinforced Metal Matrix Composites paints a vivid picture of scientific and application achievements in this field. Exploring the mechanisms through which CNTs are enhancing the properties of different metal-based composites, the authors provide a roadmap to help researchers develop MM-CNT composites and choose potential materials for use in emerging areas of technology.

Product Description
Certain interactions, such as nuclear forces and the forces of 'high-energy' physics, which arise in the theory of elementary particles, cannot be described successfully by quantum field theory. Considerable interest has therefore centred on attempts to formulate interactions between elementary particles in terms of the S-Matrix, an operator introduced by Heisenberg which connects the input and output of a scattering experiment without seeking to give a localized description of the intervening events. In this book four authors, who are together responsible for many of these developments, set out a theory of the S-Matrix starting, as far as possible, from physically plausible assumptions and investigate the mathematical consequences. The least understood of these assumptions is the vital postulate of analyticity; much insight can however be gained into its working by a study of the Feyman integrals and the book describes what is known about their analytic and high energy properties. Originally published in hardback in 1966. ... Read more

Product 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

Customer Reviews (3)

Review by me
Nice book. Many useful facts combined in one volume. Real pleasure to read it.
The only drawback is sketchy last chapter (almost no proofs due to the lack of space, I believe).

Fascinating
This book is fascinating!Bhatia has made an excellent selection of topics. It is frequently cited in the quantum information literature, and I assume also in the literature of other research subjects.This is on matrix analysis, and it has the flavor of finite-dimensional functional analysis.It is concise and has a very interesting selection of topics.

I have a few suggested tweaks for future(?) editions or classroom discussions:

Remarks on chapter 2:

The presentation at the beginning of chapter 2 would be more motivated if one operationally defines x to majorize y iff y = Ax for some doubly-stochastic matrix A.Bhatia uses an algebraic definition and then proves the equivalence after six pages later. Immediately giving an unmotivated algebraic condition robs the reader of the chance to discover or prove the condition for himself.

There is a very confusing typo in the proof of theorem II.2.8.The statement

"Let r be the smallest of the positive coordinates of x"

should read

"Let r be the smallest of the positive coordinates of y".

Another small remark: Just after the statement of Corollary II.3.4 Bhatia states that "one part of Theorem II.3.1 and Exercise II.3.2 is subsumed by [Corollary II.3.4]." In fact, they are equivalent!That II.3.1 and II.3.2 imply II.3.4 follows immediately from the following

Observation: If f:R->R and g:R->R are convex and f is monotonically-increasing then f composed with g is convex.

Notes on chapter 4:

It would be nice to have the isomorphism between balls and norms presented, perhaps just as an exercise.Then the reader can get a visual mental picture of the various conditions for a norm to be a symmetric gauge function.It might also be nice to move theorem IV.2.1 to the very beginning of that chapter, so that the reader sees the point of section IV.1 immediately.

A small remark is that the proof of Theorem IV.1.8 is made slightly more transparent by the observation that by Theorem IV.1.6 on has

[Phi(x^p)]^(1/p) = Sup Phi(xz),

where the supremum is over z such that (Phi[z^q])^(1/q)=1.(The Sup is attained when x^p = z^q.)Then Theorem IV.1.8 follows immediately from the triangle inequality and subadditivity of suprema:

[Phi(x+y)^p]^1/p = Sup Phi((x+y)z) <= Sup [Phi(xz)+Phi(yz)] <= Sup Phi(xz) + Sup Phi(yz)

Chapter 5:

Chapter 5 covers some of the most interesting and surprising mathematics I have ever seen.

Remarks:

1. All the regularity needed to classify the matrix monotone functions is already present in the case of 2 x 2 matrix monotone functions.Perhaps concretely classifying them would modularize the parts of a complicated proof, allowing some separation between discussion of operator convexity and monotonicity.(Let f:R->R be non-constant. Then f is 2x2 matrix monotone iff f is differentiable with df/dt>0 everywhere and (df/dt)^(-1/2) concave.Furthermore, the first two estimates of Lemma v.4.1 continue to hold for 2x2 matrix monotone functions.)

2.Theorem V.3.3 has somewhat restrictive assumptions: Let f:R->R be extended to a map on self adjoint matrices using the functional calculus. Then all that is needed to differentiate f(A+tH) at t=0, where A and H are self-adjoint and t is a real parameter, is for f to be differentiable on the spectrum of A.(f could be discontinuous except on spec(A), for example.)

3. I would have liked to have the definition the "second divided difference" of f at the points {a,b,c} to be "the highest-degree-coefficient of the at-most quadratic polynomial P that interpolates f on the set {a,b,c}. When a=b then one choses P such that P'(a)=f'(a) as well. When a=b=c then one also takes P''(a)=f''(a)."This is the point of exercise V.3.7, but it makes for easier reading for the definition to be conceptual and let the exercise be to work out the algebraic consequences.

Furthermore, if desired one can actually avoid this calculation and proceed to the proof of Theorem V.3.10.(Just replace f byinterpolating polynomials and evaluate everything by by algebra. It has the flavor of Feynman diagrams.)

4.In Hansen and Pedersen "Jensen's operator inequality," Bulletin of the London Mathematial Society," 35 pp. 553-564 (2003); arXiv:math.OA/0204049 (2002), the original authors of the non-commutative jensen inequality state

"With hindsight we must admit that we unfortunately proved and used [a different formulation of the noncommutatitve Jensen's inequality].However, this necessitated the further conditions that 0 is an element of I and that f(0) < 0, conditions that have haunted the theory since then."

Bhatia's presentation is somewhat out-of-date because it does not include the more up-to-date Jensen's inequality from the more recent work cited above.(Note that the more recent paper occured after the current 1996 edition of Bhatia was published.)

Furthermore, in the same paper, Hansen and Pedersen also introduce a nice version Jensen's trace inequality.It is the same as their sharper form of Jensen's operator inequality, except that both sides have a trace in front and that the operator convex function f is replaced by an arbitrary (scalar) convex function f:R->R. (f acts on matrices using the functional calculus).In particular, the trace inequality is much simpler to prove and more widely applicable although less powerful.

5. It would be nice in future editions(?) to include a reference to Petz and Nielsen's nice little proof of strong subadditivity of the von Neuman entropy.

Chapter 7:

I would have liked to see section 7.1 replaced with the following theorem statement (very similar to what's already in 7.1), and see it proved without chosing an arbitrary basis.(Using an arbitrary basis makes Bhatia's proof of the C-S theorem a bit messy, but a reformulation avoids that.)

Definition: A unitary map U on a Hilbert space is a planer rotation iff
U restricts to the identity on a subspace P of co-dimension 2, and P is unitarily equivalent to

cos(t) sin(t)
-sin(t) cos(t)

on P.

Theorem: Let E and F be distinct subspaces of the Hilbert space H, with dim E = dim F. Then there exists a set of planer rotations {R_i} with the properties that

1. The two-dimensional rotation subspaces of the R_i are mutually orthogonal and intersect E and F. (In particular, the R_i commute.)

2. Each R rotates by an angle theta in (0, pi/2].

3. E is rotated onto F by the product of the R_i.

Furthermore, the collection of angles theta_i is uniquely determined by E and F, including multiplicity. If the angles theta_i are distinct and strictly less than pi/2 then the corresponding R_i are also uniquely determined.

Further remark on chapter VII: There is an error on page 223.The author states "we have a bijection psi from H tensor H onto L(H), that is linear in the first variable and conjugate linear in the second variable".

This is impossible, since (lamda v) tensor w = w tensor (lamda w).In particular, any map that is linear in the first variable is necessarily linear in the second variable.The practice of introducing a map from H tensor H to L(H) is a cause of much ugly basis-invariance-breaking in quantum information theory and consequently should be discouraged.

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 aroundthe themes on matrix inequalities and perturbation of eigenvalues andeigenspaces. The first half of the book covers the "classical"material of majorisation and matrix inequalities in a very clear andreadable manner. The second half is a survey of the modern treatment ofperturbation of matrix eigenvalues and eigenspaces. It includes lots ofrecent research results by the author and others within the last ten years. This book has a large collection ofchallenging exercises.It is anexcellent text for a senior undergraduate or graduate course on matrixanalysis. ... Read more

Product Description
Concrete treatment of fundamental concepts and operations, equivalence, determinants, matrices with polynomial elements, and similarity and congruence. Each chapter has many excellent problems and optional related information. No previous course in abstract algebra required.
... Read more

Customer Reviews (3)

Review of Elementary Matric Theory
This book was a waste of money.The author does not know how to communicate with an average reader.So much for calling itself "Elementary" ...

Exelent clear writing
This is best mathematics book I've ever read. Eves presents his thoughts clearly and natural way, making it a comfortable reading experience.

The book has widened my understanding about matrixes.

Not Linear Algebra
I love this book. It contains a wealth of information on basic matrix theory that one almost never gets in the classroom or typical undergraduate texts. I never realised how rich the theory of matrix theory was until I read this book. Bare in mind, however, that this is not a text on linear algebra . . . the author does touch upon the subject, but even then it is linear algebra in the context of matrix theory and not matrices in the context of linear algebra. This is rather an old approach, but one I think that is very enlightening. The author touches on advanced topics such as Lie products, Hamilton products, tensor products and so on. I this way, the student learns that the traditional way of multiplying matrices is not the only way, but simply the way that linear algebra chooses to make use of the matrices. The level of the book is undegraduate, so that any intelligent high school student should be able to get much out of the book. No real math background is required, although it would be helpful. Theory is paid attention to, but a great deal of detail is also given worked out problems, making it ideal for math students who don't yet feel comfortable with advanced theoretical math. ... Read more

Customer Reviews (2)

simple, short and fine book
I like the stile and didatic of Prof. Stephenson and this little book does a good job to teach mainly matrices (the chapters on sets and groups are very shorts, however they are helpfuls). Its level is introdutory (but not properly elementary),the stuff is very well explained and the exercises are coherent with the text (they are essencial parts to learn and fix the matter).
It lacks some things like to invert matrices by the method of elementary matrices and the Jordan canonical matrices. Out that, it's almost a complete introduction.
Because it is terse and have various topics of constante use, it is also useful as a quick reference book.
I agree with the previous reviever that is best to study first some othermore elementary text to a full benefit.
Although a bit outdated, I recomend also the other books of Prof. Stephenson if there is interest in theirs contents: Mathematical Methods for Science Students,Partial Differential Equations for Scientists and Engineers, Advanced Methods for Engineering and Science Students.

Thorough, Well-Written Introduction to Matrices
I highly recommend this Dover text as either a self-tutorial or as a quick review of matrices.I initially thought that a text for the "non-mathematics science student" might prove too elementary tobe useful. It actually provides a thorough, concise (but not terse)introduction to matrices that is quite appropriate for undergraduatestudents in physics or chemistry. The sections on eigenvalues andeigenvectors, on diagonalization of matrices, and on functions of matriceswere particularly good.

I am reasonably familiar with linear algebra andmatrices and read this book partially for review, but more out of generalinterest. I was surprised at how effectively Stephenson managed in only 150pages to explore key topics at some depth without sacrificing his tutorialstyle.I am puzzled that that this book is not better known.It is quitewell-written and I give it five stars. The price is quite affordable and Idon't believe that you will find a better overview of matrices at even muchhigher prices.

Don't be concerned that this is not a new book (firstpublished in 1965).The matrix notation is modern and consistent withcurrent textbooks. The author, G. Stephenson, was Emeritus Reader ofMathematics, Imperial College of Science and Technology, University ofLondon.

I also recommend two other Dover reprints. Matrices andTransformations by Anthony Pettofrezzo is a more basic introduction.AnIntroduction to Linear Algebra and Tensors by M. A. Akivis and V. V.Goldberg is a good next step after Stephenson's text. ... Read more

Product Description

This new book offers a fresh approach to matrix and linear algebra by providing a balanced blend of applications, theory, and computation, while highlighting their interdependence. Intended for a one-semester course, Applied Linear Algebra and Matrix Analysis places special emphasis on linear algebra as an experimental science, with numerous examples, computer exercises, and projects. While the flavor is heavily computational and experimental, the text is independent of specific hardware or software platforms. Throughout the book, significant motivating examples are woven into the text, and each section ends with a set of exercises.

Customer Reviews (2)

good, could be better
I have adopted this book as one of the texts for my introductory course on applied math. It's well written and has a diverse set of good examples drawn from everything from computer graphics to sports betting. It's fun to read, and in general, good.

It is significantly better than Olver and Shakiban's book of similar title and scope, and a heck of a lot cheaper. In a course like mine where I use several specialized books rather than one of the massive tomes that try (and fail) to cover all of applied math, low price is a factor for me.

Negatives include: too few theory problems, a fair number of typos, relegation of the LU factorization to a problem set. On the whole, though, it's not bad.

Stimulating introduction to Linear Algebra
This is a very well written book. The author brings the 'topic to life' by showing how the linear algebra can be used in an applied setting. Also the graphics enable the reader to understand the material from a geometric perspective, as opposed to merely looking at terse algebraic equations.

Finally, the hints and answers section at the back of the book are very good for self study.

Highly recommended! ... Read more

Product Description
Kabbalah is a form of Jewish mysticism dating back to the first century bc. It consists of meditative, devotional, mystical and magical practices which were taught only to a select few. Today, particularly in the US, people are turning to these ancient teachings to find meaning and substance in their lives. Celebrities such as Madonna, Guy Richie, Jerry Hall, Mick Jagger, Ruby Wax, are followers, and the likes of Deepak Chopra and John Gray readily acknowledge the powerful and profound messages of enlightenment kabbalistic principles offer. Many of the books currently available today focus on the philosophy behind Kabbalah - but this book, written by a physician who has devoted many years to the study of alternative, holistic medicine - attempts to bring to a wide audience the secret of how best to create healthy, prosperous and joyous lives. Locating Kabbalah in the context of modern science, this accessible and practical guide outlines basic principles, the six keys to physical and spiritual healing and numerous exercises to help deal with specific health problems. ... Read more

Product Description
From the Preface: "Twenty years ago, noting that the basic facts about circulant matrices and its relationship to the Discrete Fourier Transform were rediscovered over and over again, I thought it might be worthwhile to publish a small book in which these facts were summarized (1979). What I did not realize was the extent to which in the years to come circulant matrices would play a role in applications and the extent to which algebraists, numerical analysts, combinatorialists and physicists would push forward the development of generalized circulants. Such matrices are now often seen as special instances of structured or patterned matrices ... The outgrowth of the simple notion of a circulant matrix has therefore been both vast and profound. Readers who are interested in applications or generalizations of circulants beyond what is given in this volume may find a ... list of publications (and their bibliographies) to be of use."

Second edition, with historical remarks and several additional references ... Read more

Product Description
This book focuses on the behavior of large random matrices. Standard results are covered, and the presentation emphasizes elementary operator theory and differential equations, so as to be accessible to graduate students and other non-experts. The introductory chapters review material on Lie groups and probability measures in a style suitable for applications in random matrix theory. Later chapters use modern convexity theory to establish subtle results about the convergence of eigenvalue distributions as the size of the matrices increases. Random matrices are viewed as geometrical objects with large dimension. The book analyzes the concentration of measure phenomenon, which describes how measures behave on geometrical objects with large dimension. To prove such results for random matrices, the book develops the modern theory of optimal transportation and proves the associated functional inequalities involving entropy and information. These include the logarithmic Sobolev inequality, which measures how fast some physical systems converge to equilibrium. ... Read more

Product Description

Matrix management was introduced in the 1970s in the context of competition from Japanese manufacturers, computerization of many technical and administrative tasks, and a recognition among business leaders that cross-functional teams (comprised of people from different departments and specialties) were necessary to create and produce complex products rapidly. Ideally, this approach, in which people are assigned to projects, rather than department managers, encourages collaboration, flexibility, and knowledge sharing, but in reality, it can often cause confusion, friction, and excessive bureaucracy. It fell out of fashion in the 1990s, but has resurfaced in a much wider array of companies today, as the pressure to innovate on ever-faster schedules encourages experimentation in organizational design.

Marvin Gottlieb, who has studied and applied the principles of matrix management for over 25 years, takes us on a tour of this phenomenon—its evolution, current practices, and future applications. He argues that most organizations are taking on characteristics of matrix structure, with fluid teams and dotted-line reporting relationships across departments and divisions. Featuring case studies of successes and failures, he shows readers how to harness the power of the matrix structure while minimizing the conflict, disorientation, and resistance that often accompany the approach. In an environment where every company—large or small, entrepreneurial or established—is wrestling with the question of how to organize for maximum performance in a harshly competitive world, this book will give leaders and managers valuable insights and tools for promoting cultures that reward creativity and teamwork while maintaining strong leadership and accountability.

Product Description
The Second Edition of this highly regarded text continuesto provide a systematic treatment of density matrix techniques. Thetext discusses basic principles and recent studies in atomic andmolecular reactions. A new chapter explores the role of orientationand alignment in molecular physics. ... Read more

Customer Reviews (1)

Needs an editor
I read most of this book while researching two-dimensional spectroscopy methods because of the literature`s extensive use of the von Neumann equation for the density operator. The beginning of this book does a terrific job explaining the basis for use of the density matrix, with essentially a worked example of the Stern-Gerlach experiment. The mechanics of time evolution are also discussed in an informative manner, as well as polarization states and coupled systems. The rest of the book treats specific applications, and I have no real complaints on the actual content.

However, this book is FILLED with typographical errors, specifically in its equations. This is unfortunate, as the Dirac notation can look confusing at times even when it is typed correctly. Add in the possibility of missing a | or a > complicates the situation. So the content is good, but the read can be difficult to execute when second guessing or needing to correct the equations. 3.5/5

Update: I found another version of this at the library which does not contain the aforementioned errors, so I'm not sure if that was a certain print. ... Read more

Product Description
Making obscure knowledge about matrix decompositions widely available, Understanding Complex Datasets: Data Mining with Matrix Decompositions discusses the most common matrix decompositions and shows how they can be used to analyze large datasets in a broad range of application areas. Without having to understand every mathematical detail, the book helps you determine which matrix is appropriate for your dataset and what the results mean.

Explaining the effectiveness of matrices as data analysis tools, the book illustrates the ability of matrix decompositions to provide more powerful analyses and to produce cleaner data than more mainstream techniques. The author explores the deep connections between matrix decompositions and structures within graphs, relating the PageRank algorithm of Google's search engine to singular value decomposition. He also covers dimensionality reduction, collaborative filtering, clustering, and spectral analysis. With numerous figures and examples, the book shows how matrix decompositions can be used to find documents on the Internet, look for deeply buried mineral deposits without drilling, explore the structure of proteins, detect suspicious emails or cell phone calls, and more.

Concentrating on data mining mechanics and applications, this resource helps you model large, complex datasets and investigate connections between standard data mining techniques and matrix decompositions. ... Read more

Customer Reviews (1)

Comprehensive and well-written!
I am doing research in data mining using tensor decompositions, and was very impressed by this book. It not only covers all of the important matrix and tensor decompositions, but also methods for computing them (with Matlab code!), the computational complexity of these methods, the tradeoffs and scenarios associated with each decomposition, and potential areas of application. To top it all off, the book is written in a highly approachable manner, covering the general concept of a decomposition and gradually discussing the specific decompositions from simplest to most complex. Highly recommended. ... Read more

Product Description

Customer Reviews (1)

A classic
Table of contents

1. SOME BASIC IDENTITIES AND INEQUALITIES
1.0 Objectives; Notation
1.1 Elementary Matrices
1.2 Some Factorizations
1.3 Projections, and the General Reciprocal
1.4 Some Determinantal Identities
1.5 Lanczos Algorithm for Tridiagonalization
1.6 Orthogonal Polynomials
References
Problems and Exercises

2. NORMS, BOUNDS, AND CONVERGENCE
2.0 The Notion of a Norm
2.1 Convex Sets and Convex Bodies
2.2 Norms and Bounds
2.3 Norms, Bounds, and Spectral Radii
2.4 Nonnegative Matrices
2.5 Convergence; Functions of Matrices
References
Problems and Exercises

3. LOCALIZATION THEOREMS AND OTHER INEQUALITIES
3.0 Basic Definitions
3.1 Exclusion Theorems
3.2 Inclusion and Separation Theorems
3.3 Minimax Theorems and the Field of Values
3.4 Inequalities of Wielandt Kantorovich
References
Problems and Exercises

4. THE SOLUTION OF LINEAR SYSTEMS: METHODS OF SUCCESSIVE APPROXIMATION
4.0 Direct Methods and Others
4.1 The Inversion of Matrices
4.2 Methods of Projection
4.3 Norm-Reducing Methods
References
Problems and Exercises

5. DIRECT METHODS OF INVERSION
5.0 Uses of the Inverse
5.1 The Method of Modification
5.2 Triangularization
5.3 A More General Formulation
5.4 Orthogonal Triangularization
5.5 Orthogonalization
5.6 Orthogonalization and Projection
5.7 The Method of Conjugate Gradients
References
Problems and Exercises

6. PROPER VALUES AND VECTORS: NORMALIZATION AND REDUCTION OF THE MATRIX
6.0 Purpose of Normalization
6.1 The Method of Krylov
6.2 The Weber-Voetter Method
6.3 The Method of Danilevskii
6.4 The Hessenberg and the Lanczos Reductions
6.5 Proper Values and Vectors
6.6 The Method of Samuelson and Bryan
6.7 The Method of Leverrier
References
Problems and Exercises

7.PROPER VALUES AND VECTORS: SUCCESSIVE APPROXIMATION
7.0 Methods of Successive Approximation
7.1 The Method of Jacobi
7.2 The Method of Collar and Jahn
7.3 Powers of a Matrix
7.4 Simple Iteration (the Power Method)
7.5 Multiple Roots and Principal Vectors
7.6 Staircase Iteration (Treppeniteration)
7.7 The LR-Transformation
7.8 Bi-iteration
7.9 The QR-Transformation
References
Problems and Exercises

BIBLIOGRAPHY
INDEX ... Read more

Product Description
Numerical linear algebra is far too broad a subject to treat in a single introductory volume. Stewart has chosen to treat algorithms for solving linear systems, linear least squares problems, and eigenvalue problems involving matrices whose elements can all be contained in the high-speed storage of a computer. By way of theory, the author has chosen to discuss the theory of norms and perturbation theory for linear systems and for the algebraic eigenvalue problem. These choices exclude, among other things, the solution of large sparse linear systems by direct and iterative methods, linear programming, and the useful Perron-Frobenious theory and its extensions. However, a person who has fully mastered the material in this book should be well prepared for independent study in other areas of numerical linear algebra. ... Read more

Product Description
Citing scenes from all three movies, Stephen Faller plugs into the richly textured and deeply interwoven network of religion, philosophy, Western values, and popular culture to reveal the films' many layers of meaning. He parallels the conceptions of Andy and Larry Wachowski-The Matrix creators-with those of such visionaries as Socrates, Descartes, Kierkegaard, Freud, Orwell, Huxley, and Spielberg, exploring the Matrix as an expression of the fears, the quests, and the dreams that human kind has struggle to define and conquer. ... Read more

Customer Reviews (5)

From the Author:
Are you interested in life beyond the Matrix? I wrote this book to explore questions of freedom and to take a serious look at the implication of the entire trilogy. You won't find an encyclopedia of the movies, but you will find a literary attempt to recreate Neo's journey into a larger world. If you want to get a taste, google the book to find the secret companion website which has additional content and more explanatory and analytic essays. No one can be told what it is...

Sorta Cliche, but at times good.
I was hoping this book might explain some of the religious and philosophical allegories of the films. It does a little of that.

Most of the book is very oriented about how you should live your life, to be free of your own personal matrices. Which is an ok message, but the book tends to get sorta "rah, rah, rah, go team" about it and keeps quoting the movies cliches over and over.

I also feel that some of the analogies to historical events were either forced, or wrong. Things like "Hitler was elected president and then became a dictator" are not entirely accurate. Sometimes the author would pull off into tangents about other movies, and I wished he would focus on the movie at hand. And sometimes, I would disagree with the author's analysis of the films as too simplistic. (i.e. I don't think he gives Smith enough credit)

Overall, there were some interesting points and analogies though, so parts of it made for good reading.

It's the question that drives us...
And that seems to be the writers motto.This book was a good grazing of the philosophy, religion, symbolism, and spirituality questions that may arise to those that see the movies as more than just a Hollywood shoot-em-up blockbuster, yet it left me with the kind of feeling you'd get from watching a two hour movie that just ended in the middle of the story, because a Part 2 was planned.It's hard to tell exactly what Faller is trying to accomplish with the reader.He often talks of "waking up" and "escaping the matrix" and defines what the matrix is in our daily lives, but I feel he failed to describewhat his opinions were about what "escaping the matrix" meant to him.I was left feeling like I had just read a book of questions, with no obvious opinions from the author to what the answers to the questions might be.There are some good points here and there, but overall I kept feeling like "ok the good part must be coming up soon when it gets more in depth."

Interesting read, but in my opinion, not a "must read".

Live the Revolution
If you thought you knew what the Matrix movies were all about - think again - and again. This book will challenge you to explore all the nuances and intricacies presented by the movies against a background of history's great philosophers. The material is presented in thought provoking comparisons by an author who speaks with authority about the great questions. This book is a must have for the Matrix enthusiast who is convinced that a movie can change their lives, but needs to understand why

To Be Awake Is To Be Alive - Thoreau
'Beyond The Matrix' by Stephen Faller
If you have seen any of the three 'Matrix' films, then you are aware of their complex nature. Afterwards, one walks around the world and wonders: 'What did that mean?' or 'What did I miss?' or 'What does that name mean?' The answers to all your philosophical and theological Matrix questions, as well as a clear road to understand this mammoth cinematic work, are contained in this delightful, concentrated book. The author, like any good philosopher, defines his terms, then takes us on a guided tour of comparitive scholarship. He takes apart The Matrix films, with their mythological names, their stark images, their suggestive dialog, and then ties them to philosophy, theology and literature in a confident, clear and thought-provoking mannner, paired with a provocative, fresh style of writing. Like Gulliver who, as a giant, takes all the ship's little ropes and pulls the fleet to shore, so this author gathers diverse images and symbols to provide us a new perspective of the three films, a view I never suspected or expected, and one which will send me back to view the films, armed with this book. I recommend this to anyone who has been affected by 'The Matrix.' You will find agreement and surprise in these pages. Mr. Faller's 'guided tour of The Matrix' is an exercise for the mind. The book will give all Matrix fans food for the journey, both through the films, and through life. If you're a fan of the Matrix films, then you must own this book. It is the best of its genre, and you will not be disappointed. ... Read more