4 comments about Topics in Matrix Analysis.

1. 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.




2. This book is a sequel to, and a worthy successor of, "Matrix Analysis". The latter was directed mostly at methods applicable to solving generic matrix problems. Whereas the present book takes a more focused view. Its topics should be understood as more specialised. Like the case where a matrix might be upper triangular and in positive or non-negative definite form. Or where certain assumptions might be made about a matrix's eigenvalues.
   
   There are some nice theorems proved about the spectral properties of various types of matrices. More to the point, the book has many useful ways to actually find the eigenvalues of such matrices. Where these methods might be more efficient than the generic methods of the earlier book.



3. This book is an excellent reference for researchers in the fields of Matrix Analysis, Numerical Analysis, Theoretical Linear Algebra, etc. I am doing currently some research involving Matrix functions and generalizations of M-matrices and I use this book all the time. Some important features of this book include the facts that 1) it is well-written 2) It is clear 3) It very useful to researchers and graduate students. It is one of those books which you can't stop reading once you start.



4. If you are communication engineer and exploring the world of channel estimation, MIMO, etc. and you need to understand the mathematical approach, you need this book. The book covers the SVD issue, which is most important for many applications.

1 comments about Matrix Groups for Undergraduates (Student Mathematical Library,) (Student Mathematical Library).

1. This book is a great introduction to matrix groups and related ideas. The author explains the basic ideas in a clear, concise, and precise way. Although there are many excellent texts on matrix groups and more abstract properties of groups, this book provides the most accessible introduction to the subject that I have found. The book is short and easy to read through, compact, and economically priced. I strongly recommend reading this book before attempting to delve into more advanced texts.
   
   The clear and unified treatment of the real, complex, and quaternion groups is *very* nice. Overall, the writing style is so lucid, it is the kind of book where you feel that the writer is teaching you personally, rather than lecturing to an empty hall.
   
   Because the book provides such an excellent introduction to the subject, I give it the full 5 stars. The book has a few typos and gaps, but most are pretty obvious. I hope that the author will expand on this book in a future edition, perhaps including a chapter on basic group theory. When you finish reading the book, your only complaint will be that it isn't longer! Given the excellent exposition, I will be on the lookout for any future texts from this author.

No comments about Matrix Algebra: An Introduction (Quantitative Applications in the Social Sciences).

No comments about Linear Algebra and Matrix Theory.

5 comments about Matrices and Linear Algebra (Dover Books on Advanced Mathematics).

1. First, the text of this book is extremely well-written, the theorems are clearly stated and the proofs are well-presented. Unfortunately, there are LOADS of typos in this book, but that doesn't bother me.
   
   What bothers me are the exercises at the end of each section - the difficulty level of several (not all) of them is far beyond the depth of the text. The text is supposed to be for "undergraduates with little mathematical experience". Don't you believe it. There are problems early in the book that ask you to write proofs that require a depth of understanding that the text does not come close to providing. Many times I was absolutely convinced that the text and the exercises were from completely different textbooks! If the author is going to include difficult or "let's see how well you got this" problems I'm all for it, but at least include some hints in the back to help students get started. Otherwise you're just stranded on your lonely little mathematical island....hungry and cold and completely screwed.
   
   If you just want a book for reference, then this is a very good choice. However, if you are attempting to learn the material and are interested in trying your hand at more than a few problems then I strongly suggest you look elsewhere.



2. As a physics major, i've been told by my E & M teacher that Linear Algebra is one of the two games to be played in physics. (The other naturally being calculus). So, what happens when it comes time to take Linear Algebra and the teacher only serves to confuse the material, and the college textbook is a normal college math book? (a.k.a. not well written or useful). Get Dover books. And this book delivers for me. Everything i'm supposed to learn in Shifrin's text is presented here with much clearer writing. (Especially in drawing your eye to the thereoms, any one who wants to Linear Algebra without knowing the thereoms or applying them to the homework should probably stop now and go back to Trig.) It seems this book would make a good stand alone text, provided you are willing to not expect calculus cookbookness, because it's my side text that trumps my main textbook for 1/10th the price. And in closing, thank God for Dover for making life as a physics major that much cheaper.



3. For about three years, I haven't thought about linear algebra at all. But recently, I've been interested in it again, and went to this book for reference.
   
   I'm lucky if I can find one nice clear example of anything in this book. This is a proof book all the way, and it's not for your general type of audience. This is bare bones stuff. That's probably why the price is 14 bucks instead of 140.
   
   Instead of getting a book like this, I recommend getting a more expensive book that's easier to understand, or just surf the internet for information. I have had some success with the latter option.



4. On my desk right now, books by: David C. Lay, Terry Lawson, Sheldon Axler, Klaus Jänich, Robert Valenza, and this one by Schneider and Barker. I tend to go back again and again here.
   I'm using this book as a supplement for the textbook in my class. Some of the books cited above don't quite fit the bill because they're so different from the linear algebra for engineering you so often see in classes. But this one is excellent for a matrix-heavy approach.
   This book is "bare bones", indeed, but it is very well written. Some might not be used to definitions, propositions, theorems and lemmas but in this case this makes it a whole lot easier for finding (and referencing) the important results. The notation is careful and formal, but the explanations are crystal clear. On the back cover it says it's geared towards students "outside the field of mathematics" but I think they say that because it avoids a purely algebraic approach (like in Valenza where e.g. Ker is defined in the context of group homomorphism). The approach is the one of matrixes, matrixes everywhere (row echelon algorithm, etc.) There are, however, no "modern" applications (such as networks, or ecology) as examples.
   Another reviewer complained about the difficulty in exercises. While you have "drill" ones, you do have more conceptual ones, but I think they're on par with the text. There are no pretty illustrations here, and you will see that you don't need them.
   In some other books, material might be presented in a wordy manner, but in this book, you just say "ah, so what so-and-so is saying is just Theorem number X.X.X in S&B."
   On the whole, this is an excellent acquisition for your undergraduate library. It is cheap and good. What more do you want?



5. This book, as already pointed by one reviewer, is filled with theorems and proofs, barely is there any application. If you wish to use linear algebra, look for another book. I found David Lay's book to be a good choice. I give it low rate not to denouce it but to emphasize this fact.

No comments about Matrix and Tensor Calculus: With Applications to Mechanics, Elasticity and Aeronautics.

5 comments about Schaum's Outline of Theory and Problems of Matrix Operations.

1. 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.




2. 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.



3. 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.



4. 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.



5. 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!

5 comments about Matrix Analysis.

1. 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.



2. I agree with other commentators who remarked that the book is better suited for someone already versed in linear algebra. For the student new to all this, the text can be, shall we say, too formidable?
   
   A good usage is when you have studied the subject, perhaps several years ago, and need a concise refresher.
   
   The strong aspect of the book is the emphasis on numerical calculations. Rather than about proving theorems. Don't worry that it was printed in 1990! While computers have heavily improved, thanks to Moore's Law, the maths of course has not. All the algorithms explained here are still germane to number crunching of linear systems. As another take, look at the Amazon page for the book, for the section about other books that cite this one. Notice the preponderance of computational books.



3. THis book covers some key aspects in matrix analysis.
   
   Would certainly recommend this book.



4. Definitely, not a lot of attention has been paid to pedagogy by the authors of this book. However it forms an excellent summary of most of the theory and is very good for one who understands it and one who wants a ready reference in the subject.



5. No matter what the blurb says this is a graduate level book. You cant teach yourself linear algebra using this book. Having said that this is a fantastic book for the initiated. Concise. Consistent. Well-written. A very helpful index. I refer to it regularly and it rarely disappoints. This is a must have. Absolutely 5 stars.

5 comments about Quaternions and Rotation Sequences: A Primer with Applications to Orbits, Aerospace and Virtual Reality.

1. This is an excellent book, it's right up there with Gilbert Strang's Linear Algebra texts.
   Want to understand quaternions and rotational matrices, well this is the book for you. Starts with the basics, coordinated transformations and such, and moves at a reasonable pace into quaternions. Others at work, looking at this book felt that they understood the text. Interestingly these were software engineers that never really gotten basic college calculus. Never could understand why many software people are so light on math. Different part of the brain I guess. Author vs. engineer.



2. Quaternions are not as intuitive as 3x3 matrices however this book give a strong understanding of quaternions so that the reader can let go of the 3x3 matrix and successfully, in my case at least, change over to only using quaternions. This has proven useful in my simulations for, and firmware code for, satellite attitude determination and control. In the version I have of this book, there are some mistakes that hopefully will be corrected, but the mistakes are obvious and easy to overlook. I hate quaternions but they are powerful tools in solving real world problems. This book made quaternions interesting and bearable. If you already have a really good understanding of quaternions, this book might help, but it has a long introduction into quaternions so you might want to review the book using the online outline to see if it actually covers more than what you might already know.



3. Book is more or less what all the glowing 4 and 5 stars say it is. I would like to add a 1859 quote from William Rowan Hamilton about his Quaternions in a note to Peter Guthrie Tait (professor and friend of James Maxwell):
   
   "Could anything be simpler or more satisfactory? Don't you feel, as well as think, that we are on a right track, and shall be thanked hereafter. Never mind when."



4. There are many other reviews that discuss (and applaud) the merits of Kuipers' treatment of the subject, and I agree with them. Rather than add a "me too", I wanted to treat some of the features of this book that make it approachable.
   
   This book is not written for the layman, you do need a fair grounding in matrix methods, complex variables, and rotations. If you remember the basics you should be fine because Kuipers reminds you of special theorems and properties as they are used. Notation is kept simple and unconfusing.
   
   Of particular note, he uses the margins in a novel way. Most math texts number their equations and refer to them often. The reader spends a lot of time flipping back and forth. Kuipers frequently puts referenced equations, needed properties, and other information in the margins where they are needed. This minimizes the usual back and forth and enables a marginally sophisticated reader to actually read and learn something new in bed.



5. Excellent book. Well written. Clear. Thoughtful.
   Plenty of examples. I would highly recommend it!

5 comments about Matrix Computations (Johns Hopkins Studies in Mathematical Sciences)(3rd Edition).

1. 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.



2. 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



3. 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.



4. 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.



5. 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.