Linear Algebra

  • W. H. Greub

Part of the Die Grundlehren der mathematischen Wissenschaften book series (GL, volume 97)

Table of contents

  1. Front Matter
    Pages II-XIV
  2. W. H. Greub
    Pages 1-4
  3. W. H. Greub
    Pages 5-40
  4. W. H. Greub
    Pages 41-81
  5. W. H. Greub
    Pages 82-97
  6. W. H. Greub
    Pages 98-138
  7. W. H. Greub
    Pages 139-161
  8. W. H. Greub
    Pages 162-180
  9. W. H. Greub
    Pages 181-203
  10. W. H. Greub
    Pages 204-243
  11. W. H. Greub
    Pages 244-278
  12. W. H. Greub
    Pages 279-307
  13. W. H. Greub
    Pages 308-337
  14. W. H. Greub
    Pages 338-367
  15. W. H. Greub
    Pages 368-427
  16. Back Matter
    Pages 428-434

About this book

Introduction

The major change between the second and third edition is the separation of linear and multilinear algebra into two different volumes as well as the incorporation of a great deal of new material. However, the essential character of the book remains the same; in other words, the entire presentation continues to be based on an axiomatic treatment of vector spaces. In this first volume the restriction to finite dimensional vector spaces has been eliminated except for those results which do not hold in the infinite dimensional case. The restriction of the coefficient field to the real and complex numbers has also been removed and except for chapters VII to XI, § 5 of chapter I and § 8, chapter IV we allow any coefficient field of characteristic zero. In fact, many of the theorems are valid for modules over a commutative ring. Finally, a large number of problems of different degree of difficulty has been added. Chapter I deals with the general properties of a vector space. The topology of a real vector space of finite dimension is axiomatically characterized in an additional paragraph.

Keywords

Multilinear Algebra algebra field linear algebra

Authors and affiliations

  • W. H. Greub
    • 1
  1. 1.Mathematics DepartmentUniversity of TorontoCanada

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-00672-6
  • Copyright Information Springer-Verlag Berlin Heidelberg 1967
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-662-00674-0
  • Online ISBN 978-3-662-00672-6
  • Series Print ISSN 0072-7830
  • About this book
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