Preface

Summary

Linear algebra is a beautiful and mature field of mathematics, and mathematicians have developed highly effective methods for solving its problems. It is a subject well worth studying for its own sake.

More than that, linear algebra occupies a central place in modern mathematics. Students in algebra studying Galois theory, students in analysis studying function spaces, students in topology studying homology and cohomology, or for that matter students in just about any area of mathematics, studying just about anything, need to have a sound knowledge of linear algebra.

We have written a book that we hope will be broadly useful. The core of linear algebra is essential to every mathematician, and we not only treat this core, but add material that is essential to mathematicians in specific fields, even if not all of it is essential to everybody.

This is a book for advanced students. We presume you are already familiar with elementary linear algebra, and that you know how to multiply matrices, solve linear systems, etc. We do not treat elementary material here, though in places we return to elementary material from a more advanced standpoint to show you what it really means. However, we do not presume you are already a mature mathematician, and in places we explain what (we feel) is the “right” way to understand the material. The author feels that one of the main duties of a teacher is to provide a viewpoint on the subject, and we take pains to do that here.