Matrix Groups (Universitext)

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These notes were developed from a course taught at Rice University in the spring of 1976 and again at the University of Hawaii in the spring of 1977. It is assumed that the students know some linear algebra and a little about differentiation of vector-valued functions. The idea is to introduce some students to some of the concepts of Lie group theory --all done at the concrete level of matrix groups.

Matrix Groups (Universitext) Review

Now hold on just a minute. A couple of things just out front: the material this book covers as concisely in one volume is not to be found elsewhere (as of December 2001). So that by itself is one of its strongest features. As for the typeset, yes it is not in a fancy TeX format with pretty commutative diagrams that most of us are used to in this day. It was not uncommon in the late seventies to have lecture notes or conference proceedings of deep importance (and the material here is) rushed to the publisher, and in the haste not too much effort being spent on the presentation. Perhaps that's off-putting to some people: particularly undergraduates or new graduate students who've not met this material before. However, if you're familiar with basic properties of Lie groups, differential geometry and some basic topology then Matrix Groups will be a pleasure to read. As for the more than occaisional errors in the original edition, this second edition is very well corrected, and has an additional chapter on root systems. Honestly, this really is a remarkable book, particularly in its uniqueness as a short and beautiful introduction to GL(n,K) and its Lie subgroups: amalgamating in with them aspects of topology (compactness, connectedness), differential geometry (tangent spaces...etc) and beyond. So if you're looking for nice TeX presentation (gothic notation and the like): you might find it difficult to enjoy the material in this volume. But is that doesn't bother you, I recommend it very strongly.

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