Matrix Computations (Johns Hopkins Studies in Mathematical Sciences)(3rd Edition)

Book Description

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

Customer Reviews:

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

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

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

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

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

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

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

Three stars are for:

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

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

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

What are the basis books for comparison?

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

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

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

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

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

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

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

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

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

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

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

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

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

Combinatorial Matrix Theory (Encyclopedia of Mathematics and its Applications)

Average customer rating:

dense monograph
An excellent treatise on applied combinatorics.

Combinatorial Matrix Theory (Encyclopedia of Mathematics and its Applications)
Richard A. Brualdi , and Herbert J. Ryser
Manufacturer: Cambridge University Press
ProductGroup: Book
Binding: Hardcover

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Graph Theory (Graduate Texts in Mathematics)

ASIN: 0521322650

Book Description

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

Customer Reviews:

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

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

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

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

Schaum's Outline of Theory and Problems of Matrix Operations

Average customer rating:

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

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

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Schaum's Outline of Linear Algebra
Schaum's Outline of Vector Analysis
Schaum's Outline of Advanced Mathematics for Engineers and Scientists
Schaum's Outline of Advanced Calculus, Second Edition
3,000 Solved Problems in Linear Algebra

ASIN: 0070079781

Book Description

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

Customer Reviews:

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

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

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

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

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

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

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

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

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

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

Book Description

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

Matrix Mathematics: Theory, Facts, and Formulas with Application to Linear Systems Theory

Average customer rating:

Where do you find that arcane result ?

Matrix Mathematics: Theory, Facts, and Formulas with Application to Linear Systems Theory
Dennis S. Bernstein
Manufacturer: Princeton University Press
ProductGroup: Book
Binding: Hardcover

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Spectra and Pseudospectra: The Behavior of Nonnormal Matrices and Operators
Matrix Analysis
Convex Optimization
Real Analysis: Measure Theory, Integration, and Hilbert Spaces (Princeton Lectures in Analysis)
General Theory of Algebraic Equations

ASIN: 0691118027

Book Description

Matrix Mathematics is a reference work for users of matrices in all branches of engineering, science, and applied mathematics. This book brings together a vast body of results on matrix theory for easy reference and immediate application.

Each chapter begins with the development of relevant background theory followed by a large collection of specialized results. Hundreds of identities, inequalities, and matrix facts are stated rigorously and clearly with cross references, citations to the literature, and illuminating remarks. Twelve chapters cover all of the major topics in matrix theory: preliminaries; basic matrix properties; matrix classes and transformations; matrix polynomials and rational transfer functions; matrix decompositions; generalized inverses; Kronecker and Schur algebra; positive-semidefinite matrices; norms; functions of matrices and their derivatives; the matrix exponential and stability theory; and linear systems and control theory.

A detailed list of symbols, a summary of notation and conventions, an extensive bibliography with author index, and an extensive index are provided for ease of use. The book will be useful for students at both the undergraduate and graduate levels, as well as for researchers and practitioners in all branches of engineering, science, and applied mathematics.

Customer Reviews:

Where do you find that arcane result ?.......2006-04-26

Sometimes it is very difficult to find out a matrix theorem that is used in a technical publication.

I have books by Gantmacher, Horn, Meyer (undergraduate), Kunze and Hoffman and Jan Magnus but if you NEED to quickly find a result, open this book. Thousands of matrix theorems and facts.

Very good reference.

Matrix Groups: An Introduction to Lie Group Theory

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Matrix Groups: An Introduction to Lie Group Theory
Andrew Baker
Manufacturer: Springer
ProductGroup: Book
Binding: Paperback

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Matrix Groups for Undergraduates (Student Mathematical Library,) (Student Mathematical Library)
Introduction to Lie Algebras (Springer Undergraduate Mathematics Series)
Lie Groups, Lie Algebras, and Representations: An Elementary Introduction
Lie Groups, Lie Algebras, and Some of Their Applications
Essential Topology (Springer Undergraduate Mathematics Series)

Accessories:

Groups and Symmetry (Undergraduate Texts in Mathematics)
The Geometry of the Word Problem for Finitely Generated Groups (Advanced Courses in Mathematics - CRM Barcelona)
Polynomial Representations of GL_n: with an Appendix on Schensted Correspondence and Littelmann Paths (Lecture Notes in Mathematics)

ASIN: 1852334703

Book Description

Aimed at advanced undergraduate and beginning graduate students, this book provides a first taste of the theory of Lie groups as an appetiser for a more substantial further course. Lie theoretic ideas lie at the heart of much of standard undergraduate linear algebra and exposure to them can inform or motivate the study of the latter.
The main focus is on matrix groups, i.e., closed subgroups of real and complex general linear groups. The first part studies examples and describes the classical families of simply connected compact groups. The second part introduces the idea of a lie group and studies the associated notion of a homogeneous space using orbits of smooth actions.
Throughout, the emphasis is on providing an approach that is accessible to readers equipped with a standard undergraduate toolkit of algebra and analysis. Although the formal prerequisites are kept as low level as possible, the subject matter is sophisticated and contains many of the key themes of the fully developed theory, preparing students for a more standard and abstract course in Lie theory and differential geometry.

The Mathematics of Matrices: A First Book of Matrix Theory and Linear Algebra

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The Mathematics of Matrices: A First Book of Matrix Theory and Linear Algebra

Manufacturer: Xerox College Pub
ProductGroup: Book
Binding: Hardcover

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Linear Algebra and Matrix Theory
Jimmie Gilbert , and Linda Gilbert
Manufacturer: Brooks Cole
ProductGroup: Book
Binding: Hardcover

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Elements of Modern Algebra
Linear Algebra and Matrix Theory
Elementary Number Theory
Matrix Computations (Johns Hopkins Studies in Mathematical Sciences)(3rd Edition)
Schaum's Outline of Theory and Problems of Matrix Operations

ASIN: 0534405819

Book Description

Master linear algebra with LINEAR ALGEBRA AND MATRIX THEORY! With coverage of the classification of bilinear forms, normal matrices, spectral decompositions, the Jordan form, and sequences and series of matrices, this mathematics text prepares you to succeed in this course and in math courses in your future. Numerous examples and exercises illustrate the theories and provide you with the practice you need to master difficult concepts.

Average customer rating:

You can't get better for 10 bucks

Matrix Theory
Joel N. Franklin
Manufacturer: Dover Publications
ProductGroup: Book
Binding: Paperback

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Elementary Matrix Theory
Applications of the Theory of Matrices
A Survey of Matrix Theory and Matrix Inequalities
Matrices and Linear Transformations: Second Edition
Theory of Matrices

ASIN: 0486411796

Book Description

Solid, mathematically rigorous introduction covers diagonalizations and triangularizations of Hermitian and non-Hermitian matices, the matrix theorem of Jordan, variational principles and perturbation theory of matrices, matrix numerical analysis, in-depth analysis of linear computations, more. Only elementary algebra and calculus. Problem-solving exercises. 1968 edition.

Customer Reviews:

You can't get better for 10 bucks.......2005-06-02

This book is a little, wonderful gem. Assuming that you know some basic stuff (that you have taken a linear algebra course and know how to deal with matrices), this will help you a lot to have a feeling of "matrix analysis".(but not linear algebra).

Matrices are widespread in all aspects of science (and especially in computer science) and if your research or work is about processing and analysing large amount of data, you cannot avoid dealing with them. I'm a graduate student in computer scince and my advisor told me that, having read that book carefully I would be equipped with basic necessary skills of matrix theory. (Yep, still reading) By the way, my suggestion is that you may skip the third chapter about differential equations and the last chapter about numerical analysis if you are not interested in these topics. But, chapters 1, 2 and especially 4, 5 and 6 are crucial.

This book is good as self study material for math, computer science, electrical engineering and decision science students who has taken suitable undergrad courses. If you are talented in math though, you may want to see the material even in undergrad or in high school. The book presents the material in a theorem-proof style which is quite nice and solid. And if you want to pursue more advanced matrix theory, you may go for a bigger book like Van Golub's book, after digesting the material in this one.

And, the best thing is that it's small and cheap. Definitely 5 stars.

Average customer rating:

Don't judge a book by its... typeset?
Don't judge a book by its... typeset?
Don't be so hard on this book
don't buy this book

Matrix Groups (Universitext)
M. L. Curtis
Manufacturer: Springer
ProductGroup: Book
Binding: Paperback

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The Classical Groups: Their Invariants and Representations

ASIN: 0387960740

Book Description

These notes were developed from a course taught at Rice University in the spring of 1976 and again at the University of Hawaii in the spring of 1977. It is assumed that the students know some linear algebra and a little about differentiation of vector-valued functions. The idea is to introduce some students to some of the concepts of Lie group theory --all done at the concrete level of matrix groups.

Customer Reviews:

Don't judge a book by its... typeset?.......2001-12-10

Now hold on just a minute. A couple of things just out front: the material this book covers as concisely in one volume is not to be found elsewhere (as of December 2001). So that by itself is one of its strongest features. As for the typeset, yes it is not in a fancy TeX format with pretty commutative diagrams that most of us are used to in this day. It was not uncommon in the late seventies to have lecture notes or conference proceedings of deep importance (and the material here is) rushed to the publisher, and in the haste not too much effort being spent on the presentation. Perhaps that's off-putting to some people: particularly undergraduates or new graduate students who've not met this material before. However, if you're familiar with basic properties of Lie groups, differential geometry and some basic topology then Matrix Groups will be a pleasure to read. As for the more than occaisional errors in the original edition, this second edition is very well corrected, and has an additional chapter on root systems. Honestly, this really is a remarkable book, particularly in its uniqueness as a short and beautiful introduction to GL(n,K) and its Lie subgroups: amalgamating in with them aspects of topology (compactness, connectedness), differential geometry (tangent spaces...etc) and beyond. So if you're looking for nice TeX presentation (gothic notation and the like): you might find it difficult to enjoy the material in this volume. But is that doesn't bother you, I recommend it very strongly.

Don't judge a book by its... typeset?.......2001-12-10

Now hold on just a minute. A couple of things just out front: the material this book covers as concisely in one volume is not to be found elsewhere (as of December 2001). So that by itself is one of its strongest features. As for the typeset, yes it is not in a fancy TeX format with pretty commutative diagrams that most of us are used to in this day. It was not uncommon in the late seventies to have lecture notes or conference proceedings of deep importance (and the material here is) rushed to the publisher, and in the haste not too much effort being spent on the presentation. Perhaps that's off-putting to some people: particularly undergraduates or new graduate students who've not met this material before. However, if you're familiar with basic properties of Lie groups, differential geometry and some basic topology then Matrix Groups will be a pleasure to read. As for the more than occaisional errors in the original edition, this second edition is very well corrected, and has an additional chapter on root systems. Honestly, this really is a remarkable book, particularly in its uniqueness as a short and beautiful introduction to GL(n,K) and its Lie subgroups: amalgamating in with them aspects of topology (compactness, connectedness), differential geometry (tangent spaces...etc) and beyond. So if you're looking for nice TeX presentation (gothic notation and the like): you might find it difficult to enjoy the material in the is volume. But is that doesn't bother you, I recommend it very srongly.

Don't be so hard on this book.......2000-12-01

Evan Morgan was unduly hard on this book. True the typsetting is bad, but its not unreadable. I learned a lot from this book. It develops matrix group theory from very few prerequisites. I have one complaint: the problem sections seem unrelated to the chapters, but all in all I learned a lot from this book and found it very helpful.

don't buy this book.......2000-04-02

The typeface of the book is courier and appears to have been originally written on a typewriter and then photocopied. This is a nuisance. The notation they use is terrible (thanks to the typewriter). More importantly, the explanantions and proofs of ideas and theorems are not good at all. I think the book was copied directly from some professors lecture notes (for a course he has taught 30 times already) which makes every thing very cryptic. Good luck learning anything from this book.

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