Review by Choice Review
A mature approach to linear algebra. Assuming very little by way of prerequisites, Curtis develops standard topics in linear algebra (e.g., matrices, vector and inner product spaces, linear transformations, diagonalization, spectral theorems, and Jordan form) plus enough abstract algebra to culminate his book in a proof of Hurwitz's theorem (that the only normed algebras over the reals are the real numbers, the complex numbers, the quaternions, and the octonions). The result is an elegant book that is a marked departure from, and considerably more advanced than, the current crop of elementary-level books. No applications and a high level of abstraction make this book an interesting (and perhaps more demanding) alternative to works such as K. Hoffman and R. Kunze, Linear Algebra (2nd ed., 1971). There are exercises at the end of each section plus additional ones scattered through the text as appropriate. Recommended for mathematically sophisticated undergraduates or graduate students of pure mathematics who wish to think about linear algebra once again. -S. J. Colley, Oberlin College
Copyright American Library Association, used with permission.
Review by Choice Review
