Matrix Algebra: Theory, Computations, and Applications in Statistics [Hardcover]

I am not a real mathematician or hard core numeric analyst; my formal training is lacking, and maybe that's why I don't gravitate to Dennis Bernstein's text or others like it. I have managed to get past the very basics (rank, determinants, permanents, spectral decomposition, Jordon normal form) and come to appreciate the numeric issues involved in computing (or, more to the point, avoiding the computation of) inverses and pseudoinverses. The theory is less interesting to me than, or at least is primarily in service of, the applications. James Gentle's treatment of how numeric computing is actually done serves as useful context which I found missing in some more theoretical texts, and glossed over by some introductory texts. I guess that's why I keep coming back to it. It serves my personal needs. I find it surprisingly readable; diagrams are used as needed, and its index is good.

Perhaps I am simply in a sort of limbo, where this intermediate (?) linear algebra text is something I might eventually outgrow. (When that might happen, I'm sure I don't know) Experienced numeric analysts seem to prefer treatments like Bernstein, Horn, or Golub & Van Loan, while the SIAM text by Meyer or the classic textbooks by Strang are probably better introductions. This book is clearly slanted towards statisticians, and more than that, statisticians who find themselves operating on large datasets, perhaps without a rigorous math background. It was invaluable to me when I had to implement my own GLM engine (for reasons too boring to discuss here, I couldn't use GPLed software). You don't really need it to peck at R, for example, but if you go to scale up a piece of code in C++ or similar, it will be much more difficult if you haven't digested this material. (I find Jorge Nocedal's "Numeric Optimization" to be an extremely useful companion to Gentle's book)

It's cheaper (on Amazon, at least), and to my mind more coherent, than any of the other texts I have listed above. Our university library is superb, so I've checked out all of them, and I own Meyer's book. (It was very useful for me to get started and I wish I'd had it when I took p-chem) But now Gentle's book is the one on my desk (library sticker and all -- I still haven't bought it, though I've had it out on loan for something like 10 months now). I doubt that a physicist will learn anything new from it, but a CS student might. Gentle has a newer textbook out on Computational Statistics, so depending on your focus, that may be of equal or greater value to you. I can just read papers (or look for implementations) if I need specific solutions; this book helps me organize different methods by theme, and provides just enough rigor for me to maintain mathematical context.

If you are in a similar situation, I think you'll find this book to be a valuable resource. I have.

I think it's one of the best books on the subject, all theorems with demonstration, a lot of examples and problems solved (I like specially the chapter about Generalized Inverse matrix)... ...written in Latex so it looks very "beautiful"...ALL what you wanted to know about matrix theory is in this book ... very rigourous, with modern notation for matrices and vectors, besides it covers almost all subjects related with the application of matrix theory (...for a statistician who works in multivariate analysis or linear models this book should be THE BIBLE...).Besides it is much modern than many of the good books in the subject (Gantmacher for example). I love this book

It deserves SIX stars. Very briefly:
I came across several books of matrix algebra. This is probably the most comprehensive, captivating and informative.
In case of doubts or needs of research about any issue on matrix algebra and methods for analyzing/computing multivariate structures, this is the place to go.
Nothing is missing.
It is not structured with definitions, lemmas, theorems, corollaries. It explains and clearly *proves* every concept in a talkative manner, extremely formal yet. When things gets complicated, it always refers to the proper paragraph for helping the reader to connect the dots.
Computational solutions are described in strict mathematical words (no pseudo code) step by step.
Overall, this is a wonderful piece work.