No comments about Introduction to Quadratic Forms (Classics in Mathematics).

No comments about Lectures on Matrices (Phoenix Edition).

1 comments about Matrix Algebra & Its Applications to Statistics & Econometrics.

1. It appears that some statisticians don't get a good grounding in linear algebra. At least, that is the contention of the authors, who have proceeded to write a linear algebra text, with an emphasis on statistics and economics.
   
   Much of the text offers little new from any standard text on linear algebra. The topics include linear transformations and matrices, Euclidean spaces, unitary mappings, projection operations onto subspaces, idempotent operators... There is a slight discussion on various inequalities useful in statistics.
   
   But overall, if you already have a text on linear algebra, this may be superfluous.

No comments about Non-negative Matrices and Markov Chains (Springer Series in Statistics).

No comments about Matrix Calculus and Zero-One Matrices: Statistical and Econometric Applications.

No comments about Lambda-Matrices and Vibrating Systems.

2 comments about A Course in Metric Geometry.

1. The authors present a self-contained treatment of the geometry of length spaces. They begin with the definition of length spaces, and by the final chapter cover almost all of the material in the well known survey paper by Burago, Gromov, and Perel'man. Overall, the book provides an interesting and and accessible introduction to an important class of spaces (length spaces arise as limits of sequences of Riemannian manifolds). I found it exceedingly interesting that one can build analogues of most of the concepts from Riemannian geometry using only the intrinsic metric. There is great emphasis on exposition in this book; Burago makes great effort to motivate definitions and provide interesting examples. The reader is cautioned, however, that numerous typographic errors are to be found (some in fundamental definitions).

   My only complaint is the uneveness of the treatment. The authors spend two chapters developing some of the basic tools of Riemannian geometry in the setting of surfaces in R^3. It seems unlikely to me that a reader who is interested in length spaces would not already have at least passing aquaintence with Riemannian geometry. This, however, is a minor point, and I can recommend the book very highly.




2. I am an undergraduate math student, and I encountered this book as the primary background text for a summer project in geometry. I had just been through a year or so of studying manifolds and basic Riemannian geometry, but it was my first substantial exposure to the length space approach to geometry as well as notions like curvature/Alexandrov spaces, polyhedral spaces, the hyperbolic plane, and quasi-isometries. It does a number of things very well, but it does possess some comparitively minor flaws that are nonetheless worth noting.
   
   Pros: The definitions and examples are very clearly explained and in a manner highly suitable for self-study. The exercises are challenging and they do a great deal to get the reader's hands dirty and force him/her to really process the main ideas. Most of the proofs are very well written, and the authors do a good job of demonstrating the appropriate tools and outlining the best approaches in the proofs and the examples. The authors also do a good job in general of summoning the neccessary background material without dwelling on review too extensively; you should probably have already seen the Hausdorff measure and the fundamental group before you pick up this book, but the book recalls the main concepts and results (with helpful exercises) in case your memory has faded or don't have much experience with such notions. Even the review of Riemannian geometry, which might be too long for some, is appropriate to firmly establish notation and because hyperbolic geometry and Riemannian curvature are so central to the topic of the text.
   
   Cons: Some of the key definitions and proofs (such as the triangle criterion for nonpositive/nonnegative curvature) contain typos, but for the most part they are sufficiently obvious that a critical reader will be able to figure out how to fix them with minimal confusion. While most of the proofs are easy to follow (especially the more technical proofs where lack of clarity would be a serious problem), some of the more visually-oriented proofs are very poorly written and there are precious few diagrams to compensate - see, for example, the example involving the curvature of cones over circles of various lengths. Also, the book could use some more exercises to accompany the more technical constructions. The exercises that it has are very well-chosen for the purpose of forcing the reader to internalize the relavent concepts and techniques, but some basic definition chasing to help process the harder definitions would make the process go smoother.

No comments about Matrix Theory: A Second Course (University Series in Mathematics).

No comments about Spectra and Pseudospectra: The Behavior of Nonnormal Matrices and Operators.

1 comments about Introduction to Matrices and Vectors.

1. Just a quick review to warn people like me who buy books like these to help us in our autodidact pursuits. I bought this Dover book because I trusted Dover publications and am now disappointed to say that this trust is now in question. The book has some merit: the flow and examples are clear and well laid out however, THERE ARE NO SOLUTIONS TO THE EXERCISES!
   Be aware that there are some glaring mistakes even to the beginner's eyes. For example, the author says "We may determine a 4X4 matrix..." and then represents this 4x4 with a 5x5 matrix. And he contradicts a commutivity theorem by saying that where two matrices A and zero share the same nxn row & column dimensions An+0n=A and then right after this he says A+0=0 on pp. 12-13. This is wrong! How am I supposed to trust further examples from this book? Sorry, I'll have to permanently shelve it...
   Good luck.
   IndiAndy
   Aspiring Autodidact