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.

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.

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.

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

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.