Lectures in Abstract Algebra

II. Linear Algebra

  • Nathan Jacobson

Part of the Graduate Texts in Mathematics book series (GTM, volume 31)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Nathan Jacobson
    Pages 1-30
  3. Nathan Jacobson
    Pages 31-62
  4. Nathan Jacobson
    Pages 63-114
  5. Nathan Jacobson
    Pages 115-135
  6. Nathan Jacobson
    Pages 136-171
  7. Nathan Jacobson
    Pages 172-198
  8. Nathan Jacobson
    Pages 199-226
  9. Nathan Jacobson
    Pages 227-237
  10. Nathan Jacobson
    Pages 238-276
  11. Back Matter
    Pages 277-280

About this book

Introduction

The present volume is the second in the author's series of three dealing with abstract algebra. For an understanding of this volume a certain familiarity with the basic concepts treated in Volume I: groups, rings, fields, homomorphisms, is presup­ posed. However, we have tried to make this account of linear algebra independent of a detailed knowledge of our first volume. References to specific results are given occasionally but some of the fundamental concepts needed have been treated again. In short, it is hoped that this volume can be read with complete understanding by any student who is mathematically sufficiently mature and who has a familiarity with the standard notions of modern algebra. Our point of view in the present volume is basically the abstract conceptual one. However, from time to time we have deviated somewhat from this. Occasionally formal calculational methods yield sharper results. Moreover, the results of linear algebra are not an end in themselves but are essential tools for use in other branches of mathematics and its applications. It is therefore useful to have at hand methods which are constructive and which can be applied in numerical problems. These methods sometimes necessitate a somewhat lengthier discussion but we have felt that their presentation is justified on the grounds indicated. A stu­ dent well versed in abstract algebra will undoubtedly observe short cuts. Some of these have been indicated in footnotes. We have included a large number of exercises in the text.

Keywords

Calculation Morphism algebra linear algebra mathematics

Authors and affiliations

  • Nathan Jacobson
    • 1
  1. 1.Department of MathematicsYale UniversityNew HavenUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4684-7053-6
  • Copyright Information Springer-Verlag New York 1953
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4684-7055-0
  • Online ISBN 978-1-4684-7053-6
  • Series Print ISSN 0072-5285
  • About this book